The part that smells this fishy to me is that she’s coming out now at the same time she’s trying to achieve a lesser sentence. I wouldn’t look too much in how she looks in mug shots and stuff, as it’s not uncommon for a trans person to heavily overcompensate if they’re trying to hide who they are (or have trouble accepting themselves).
However, because this person is on the extreme right, and the extreme right loves to go on about how men could game the system by pretending to be women, and the fact that this particular individual seems to be trying to, well, use the system to get a lesser sentence, I do think skepticism is warranted. This isn’t someone coming out of their own accord, with no benefit other than no longer being misgendered.
Given this situation, I would say that you would need the same evidence that a doctor would look for before helping someone who identifies as trans to be able to medically transition. Granted, the “live as your preferred gender for a certain amount of time” part would be more difficult in a male prison, but those sorts of restrictions come with committing the crime. You have an opportunity to see if she slips up.
If she really is committed to this, then let her change prisons—but no change in sentencing whatsoever. And, of course, you can enforce standards of dress and such. And, again, if she slips up, then you’ve caught her in the lie, and you can add appropriate punishment for trying to game the system.