Really... I would just as soon do the two character bit with the change being a meta sort of thing as you suggest, but the group really wants to see it in action from a game mechanics view. They're really wanting to see how such a complex (and odd) phenomenon can be explained with extant rules (don't have the Paranet extension yet).
In this case, I would stress the above solution again. All that this is accomplishing is to give an ingame solution for an outgame problem. Unless the character is able to shift back and forth at will, meaning one player could play both characters, it's not worth charging refresh for. In fact, charging refresh for it would be a penalty to both players, since that would mean they can take less other powers because of their work schedules. I think that's an important thing to drive home. Not everything that's happening has to be put into mechanics, especially if it's just a flavor thing, as it is in this case.
If there are benefits they get from this, you should absolutely let them pay for it. But as long as it doesn't, there's definitely no need. So if it were a single character powers would make sense, since that's part of the character. But in this 2 player solution, I would advise against it.
So let's say she's not too good at shooting guns, while he was a master marksman. If you add on demonic copilot, she could draw on his expertise to be a better shot. Likewise, he could draw on her expertise when hacking into a computer system. Or any other situation that might fit. Demonic Copilot would absolutely make sense there. But if it's just to say "the character is possessed, it needs to have a power for that", no. That's what aspects are for. They are just as much a game mechanic as anything else.
If you go with a possession, that might complicate matters in terms of plausibility when it comes to shapeshifting. Why would his soul impose his physical form on the body he's possessing? I mean, sure, it absolutely can, but it seems weird without an explanation. A story explanation that is, not a mechanical one.
Are they related in any way? Blood of my blood, add some magic, boom? That might be a decent enough explanation how this would be possible.