Was "UTA III - Reincarnation" in the original Ghost in the Shell movie?
I do believe so, Kenji Kawai's soundtrack was released on November 22, 1995, and it does contain the track "UTA III - Reincarnation".

All three contain the track: 


https://itunes.apple.com/gb/album/ghost-in-the-shell-koukaku-kidoutai-original-soundtrack/910532068
http://wrwtfww.com/album/ghost-in-the-shell-original-soundtrack
https://www.amazon.com/Ghost-Shell-Kidoutai-Original-Soundtrack/dp/B00MVNA8F6


When Ghost in the Shell 2.0 was released, an updated version of the soundtrack was released on December 17, 2008. This also contained "UTA III - Reincarnation"