When I read 'transwoman', I read 'male'. I guess it's similar to 'drag queen' as a word/phrase, in that I understand the meaning to be 'male'.
Some prefer 'trans identified male', yep. I don't think we're allowed to use the acronym on here, though.
The identity of the person involved is absolutely crucial, though, and I think here it is perhaps most clear when we use the word that trans activists use, too, because we are told repeatedly by people like Nicola Sturgeon/Shona Robison that "abusive men are the risk to women, not transwomen" and :
'“there is no evidence that predatory men have ever had to pretend to be anything else to carry out predatory behaviour".'
twitter.com/andrewdoyle_com/status/1500594329139748865?lang=en
This is a very clear - and upsetting - case that illustrates the issues with both of those positions.