I don't think it's Morrigan. Because that does not make sense in my eyes. Morrigan never willingly accepted Mythal's soul to "invade" her body. But Flemythal clearly says "A soul is not forced on the unwilling". So I see no way for Morrigan to inhabit Mythal's soul now. Also, I am not so sure if "Mytahl's soul" and "Mythal's power" can be separated. So at the end we meet Flemythal and Solas; and Flemathyl must still have Mythal's soul. If the soul had left and we only saw Flemeth there, shouldn't she die in an instant anyway? She is ancient by now and only kept alive by Mythal's soul being in her body. The moment the soul leaves the body, it collapses. So the soul should be in Solas now.
Sure, the authors said "he takes her power" but maybe that's just a matter of words and not one of meaning.
I humbly disagree. I also don't think it's Morrigan and I don't think Morrigan has Mythals soul, yet. We know Mythal can survive without a body, she became a wisp to find Flemeth after all, not to mention in DA2 she says something like, "Must I have a body, they are such confining things" (or something similar). Plus, in that same stroke we learn she can store a piece herself in an object and that is enough to revive her later. Hence she seemingly can be in two places at once. Not to mention Solas' power (or perhaps some of Mythal's) seems to be separated from their souls (the orb), so we seemingly have evidence that it can happen.
Not to mention that drink from the well or not, become a dragon or not, Mythal does something to Morrigan both times. The only time she doesn't is with Kieran around in which case she had plenty of time to do what she did with Morrigan in that scene to him instead (yes, I've played all these possible scenarios).
So I don't think Morrigan got Mythal's soul in that moment but I believe she or Kieran were marked in some way for Mythal's soul to find her/him later, in order to offer her a deal or something. Considering Kieran says that Morrigan is going to be "the inheritor of the new age" I believe that is what they have planned for Morrigan.
Furthermore not only did the dev notes say Solas took Mythal's power but we also see a soul transfer with Kieran, and it doesn't look anything like what is going on with Solas and Flemeth in the end. Not to mention, as I've stated before, I doubt Solas would risk taking Mythal's soul, she is apparently more powerful then him and he would risk losing himself and getting overwhelmed. And considering how upset he is you "give up a piece of yourself" when you drink from the well it is somewhat hypocritical for him to do the same.
So why did Flemythal die in the post credit scene if he only took her power? Well, speaking simply we can look at a mage, if they use up all their power/mana they die of exhaustion or something like that, so we can probably assume that if we drain the power we kill the body.
Or I could be wrong and you could be right, neither of us knows for sure of course, I'm sure we'll find out sooner or later though, I just wanted to get my two cents in.
Plus we already had one possessed apostate LI in Anders and I'd rather not see that happen to another.
I personally am no fan of this "He wanted to tell her but chickened out" approach, but if I do assume it to be true then he obviously did not mean to leave. Now he realizes at some point that he doesn't have another option but to go and not tell anybody about his identity and plans.
In the end it does not even matter when he decided to break up, before the vallaslin scene or "during" it. (1) If he decided it before, maybe he wanted to give something to Lavellan as a farewell present -- being the person he is, he considers truth (in this case the truth about the vallaslin) a gift after all. Or (2) if he decided to break up because he chickened out, his decision to leave might have occurred right there or even later still.
I agree with the "he never actually used Lavellan or was planning to leave the whole time" thing. However I wonder if you really need to assume if the "he wanted to tell her but chickened out" is true or not. We already have word of Weekes it is true from that podcast.
I believe it basically went, he wanted to tell her, chickened out, contemplates giving up his mission, decides he can't give up his mission and has to cut emotional ties with Lavellan (this part Patrick Weekes already confirmed in that podcast), but I still don't think he decided to leave there.
At this point he still believes he is going to get the orb back, and whatever that orb does was probably his "quick fix" to whatever it is he had planned. He probably intended to use it as soon as he got it back, hence the "after the final battle all will be revealed" line, and then see if Lavellan would forgive whatever it is he was going to do, but then the orb got destroyed and then he decided to leave. "It was not supposed to happen this way."