That is, a transgender man would not be a man who became a woman, but a woman who is now a man?
Audrey & Sophie are women. A transgendered man was,usually, once, physically, a woman. A transgendered woman was, usually, once, physically, a man.
I say 'usually' because as society becomes more open about this stuff it is becoming increasingly clear that gender is a sliding scale, not a binary state. A surprisingly large percentage of the population people are born somewhere on the scale between male and female physically (and/or mentally).
Hopefully we'll just get over gender. It's essentially an unhelpful social construct that is too rigid for nature.
For a transgender person, one's gender is always what it is; it's just the body that might need adjustment. Also, it's hard to say when one's "arrived" anyway; there's not really a point when you just say "tada!" and you're all done. It's a very gradual process.
Some trans* people will still rrefer to themselves as trans* even "after" transition (inasmuch as you can pinpoint an 'after') because they internalise that as part of their identity; others don't.
> a transsexual man is a person who was assigned the female sex at birth [but] identifies as a man and is transitioning or has transitioned to a male gender role and has or will have a masculine body.
They're separate components of the person's identity: a transgender man is a man and transgender. From [it is common courtesy to refer to a person as their current preferred/identified gender] it follows that a transgender man is transitioning, has transitioned or will transition to masculinity.