You are asking about an Interstate Compact. It is something that your friend can't handle alone. He can request one, but the sending state(PA) can deny it and not submit the paperwork. The PO may not be able to get his request entertained by his superiors. The parole board may have rejected it. Even if PA sends the request FL can and in most cases, will reject his request.

But, the institution has to send a request for transfer and it sounds like he does not qualify for some reason.