It’s a good movie trying maybe to be too much. The acting is good and the premise is interesting, but I didn’t feel it really went anywhere. Also, I didn’t feel like they tied the ‘discovery’ (of the lesson) into the other characters well enough.
So they set us up well and sorta left us hanging.
IMO, he’s from K-Pax. He knew too much science, disappeared from the institution for a while, Bess was missing at the end, he was ‘in character’ even when hypnotized, etc. Hard to say, but that’s what I’d have to guess. However, they clearly left it open for a reason so figuring out for sure isn’t necessary to me.