Both short films (the first is 54 minutes, the second is 60 minutes) were originally released in the Japanese cinema as double bills with other short films.  However the second film is so tightly linked to the first that it they should really be reviewed as a single entity.
Silent Möbius itself is a long running manga created by Kia Asamiya. The manga itself is gorgeous, albeit very heavily influenced by Blade Runner . It is however much more of a fantasy as there is a significant amount of magic, spirits, and demons running along side the high tech  and the psionics.
The movies provide yet another approach to the manga or series adaptation: the prequel episode . This allows the two films to focus on the recruitment of the eventual hero(ine) Katsumi Liqueur into the five-team.
It is safe to say that this isn't, initially at least, handled particularly well by the nascent Attacked Mystification Police Department .
But enough initial rambling, on with the show(s).
The first film starts in 2028 with the fully formed AMP being called to the site of the Tokyo Orbital Elevator Spirals  as there is a supernatural incident going on. The initial scenes (briefly) showcase the talents of each team member - the cyborg Kiddy Phenil, the Shinto Priestess Nami Yamigumo, the Visionaire Lebia Maverick , the psychic Yuki Saiko, and the increasingly powerful sorceress Katsumi.
However as Katsumi begins to fight the particular Lucifer Hawk responsible for the incident, she realises that she has been here before and experiences a flash back. It is now 4 years earlier and a 19 year old Katsumi is returning to Japan from Hawaii to visit her mother in hospital.
Events move quickly as the otherworldly beings, the Lucifer Hawks, begin to descend on Katsumi seeking her hidden powers. The AMPD moves to "protect" Katsumi, but their introduction is fairly badly handled and Katsumi rapidly enters a state of denial.
At this point Katsumi is a classic horror movie victim  with very little agency: she is the target, not the weapon. At this point her powers are still under a seal placed by her mother Fuyuka that serves to hide Katsumi to a point. It helped that Fuyuka sent Katsumi away from Tokyo , but summoning her back so that Fuyuka can unseal her powers only reinforces how little agency Katsumi has at this point.
It is Fuyuka who is the true heroine of the first film. From the beginning it is clear that Fuyuka is dying, and the effort of shielding Katsumi is pushing her to the brink. Despite this Fuyuka travels to the foundation of Spirals (under construction at the time) to conduct a blood magic ritual  that will:
a) Kill her;
b) Draw the Lucifer Hawks away from Katsumi; and (just for good measure)
c) Unseal Katsumi's powers.
As the ritual begins to work Rally Cheyenne, the AMP Chief, picks up Katsumi and brings her to the building site . This is where Katsumi is presented with the opportunity to enter the ritual circle and awaken her powers. Katsumi does so and manages to banish the Lucifer Hawk, but is unable to save her mother.
At this point the flashback ends and Katsumi realises that she is facing the same Lucifer Hawk from 4 years ago. This time the Lucifer Hawk is not constrained by the blood magic ritual and basically treats Katsumi like a pinata.
Then, amidst the property damage, Katsumi finds the knife her mother used. This is when Katsumi performs a blood ritual of her own (courtesy of wounds already inflicted)  and manages to use the ritual and the effectively enchanted knife to end the Lucifer Hawk. In the process Katsumi also ends the orbital elevator .
This feeds into the end credits as the sun sets, the lights of Tokyo come up... and a giant magic circle appears over most of Tokyo.
In turn the second film opens with the magic circle leading into gloriously well animated sunrise . This seamless integration into the ending of the first film is slightly ruined by the fact that we are back in the flashback timeframe.
Katsumi is grieving for her mother, and is again firmly back in denial.
If the first film was dominated by the presence of Fuyuka, the second is dominated by the absence of her father Gigelf. This is not helped by her Lebia, at Fuyuka's request, handing Katsumi a book written by Gigelf on magic. This tangible link to a mysterious, always absent, figure only serves to confuse the already grieving Katsumi further.
Being denied exit from Japan, and effectively being drafted into the AMP as a "messiah" doesn't help. Katsumi wants to go home, and doesn't care about the nameless people in Tokyo.
Meanwhile there are Lucifer Hawks helping to drive her despair, particularly with one tragic scene involving the death of a child that had amused Katsumi in the street. This is a harrowing scene, and well handled.
At this point Katsumi has basically been smashed down to the bedrock, and more or less wants to die. This is where Katsumi flees the AMP into the rain.
Enter Saiko Yuki who is among other things an empath and a genuinely nice kid . Yuki rescues Katsumi from the acid rain and begins to connect with her.
However Katsumi is still seeking home, or something that was home once, and flashbacks to Tokyo Bay lead her to the mother's old home...where the Lucifer Hawks have taken up residence.
Despair, mayhem, and regaining herself ensues. Oh, and urban renewal courtesy of Lebia's orbital laser. 
The climax of the second film is essentially all about Katsumi gaining agency. It is about her realising that she does have friends, and about accepting that her magic can be used to protect them. In essence it is about stopping trying to connect with a father that isn't, and will never, be there and connecting with friends who are here now.
The final battle is where the earlier heavy handedness of the AMP transforms into the loyal defence of a valued friend.
Ultimately the second film is about friendship, and although a little rushed , works well on this level. It helps that Yuki is so persistent about it. 
In a very nice touch the finale neatly segues into the opening chapter of the manga, which ties off the prequel neatly.
The animation in both films has stood the test of time remarkably well. There are occasional moments when the age is noticeable, but for the most part that old sensawunda is still there.
The Kaoru Wada soundtracks to both films are just purely astonishing, although that duet  means that the second OST is the one I prefer.
I watched both films tonight with a housemate. Although he enjoyed them, and was mostly able to follow what was going on, these films do show the typical problems of adapting long running manga into theatrical releases. There is so much that is only alluded to that there can be problems with comprehension.
I think that the prequel approach does counter this to an extent, but the problem is still there. As I recall I first encountered these films before the manga, and have always adored them.
And even though I've been looking at Katsumi somewhat more critically this time around, there is still that core of heroic women that made me go "wow" all those years ago. It also helps that Yuki is the only underage character of significance: this is a show about adults which is always something I appreciate.
Unlike Macross : Do You Remember Love, the Silent Möbius films have lost none of their impact, and I thoroughly recommend them.
Day 1 - New Kimagure Orange Road: Summer's Beginning (1996)
Day 2 - Naruto Shippuden The Movie (2002)
Day 3 - Galaxy Express 999 (1979)
Day 4 - Steamboy (2004)
Day 5 - Urusei Yatsura 2: Beautiful Dreamer (1984)
Day 6 - Lupin III: The Castle of Cagliostro (1979)
Day 7 - Howl's Moving Castle (2004)
Day 8 - Ah! My Goddess: The Movie (2000)
Day 9 - Summer Wars (2009)
Day 10 - Macross: Do You Remember Love? (1984)
Day 11 - Silent Mobius I & II
Day 12 - ???
Day 13 - ???
Day 14 - ???
Day 15 - ???
Day 16 - ???
Day 17 - ???
Day 18 - ???
Day 19 - ???
Day 20 - ???
 It has been a while since the last entry in this series but I've been overdosing on new material recently.
 If memory serves me The Heroic Legend of Arslan and The Weathering Continent respectively.
 Seriously. A crossover between the two would require very little stretching on the part of any author.
 As mentioned later in the review, Lebia has her very own orbital laser. Urban renewal from orbit...
 I've previously discussed the plot summary, direct sequel, slightly alternate universe, and the "continuity? what continuity?" schools of adaptation. Most of which have examples in the previous posts in this series.
 I've also seen it translated on occasion as the Abnormal Mystery Police Department which is somewhat better...but doesn't help when the original wording appears, in English, on the badges in the manga and anime. :)
 Personally that's the last place I'd put a beanstalk.
 Which in Lebia's case means: I can set you up the bomb. All your net are belong to me.
 Complete with an attack in a shower. Tentacles and Anime anatomy applies.
 Aka the hellmouth.
 Apparently Fuyuka had a LOT of blood to go round. And also, blood magic? That rarely ends well.
 In some style: Rally's personal ride is a flying Rolls Royce.
 This being one of the times when blood magic does end well. More or less, and excepting a trip to hospital for Katsumi.
 Sometimes Katsumi completes with Kei and Yuri for property damage. Having Yuki's visions to assist with early evacuations is kind of helpful. :)
 Surprisingly so. It still stands up well despite being nearly 20 years old.
 One nice touch in Silent Mobius is acknowledging the cultural origins of the characters in their names. The Japanese characters will have the family names first, the western characters will have the reverse. Katsumi is (at least technically) the latter as she identifies as an American initially.
 You thought I'd forgotten about that. By the way her satellite is called Donald. Her other three AIs are called Huey, Dewey, and Louie.
 60 minutes doesn't really leave a lot of room for character development.
 I wouldn't say that Yuki nags Katsumi per se, but it was close.
 Which I'm listening to right now. Because I can. :)
NB: There are quite a lot of spoilers in this long review. Also many footnotes of varying degrees of snark. :)