Even in the UK there's no way she'd get into a womens prison, even if she were to self id as a woman.
Forget about trans. There are about 14,000 male sex offenders in prison at the moment. How many of them would think it prohibitive to self ID? By downloading a form.
It currently costs £140 but there is a waiver if you can't afford it.
(And it should cost money. Somebody is being paid to process the work. They're not doing it for free.)
Potentially 14,000 men happy to tie up the system, at the very least, and at the very best, get transferred to the female estate.
So say they bring in some kind of assessment to find out whether or not the person is a danger to women.
And, at the very least, the female estate will be inundated with men. There are currently 5000 women overall in prison, almost half of whom have suffered some kind of sexual trauma.
And what for?
To validate a man's identity?
Because, you can bet your life, there will not be a queue of transmen clamouring to get into the male estate.