You don’t need to put the asterisk after the words trans and male. Trans men are men whether or not they take the “steps” to “become” any particular way. Their boyfriend should not be using any pronouns besides the ones the person in question asked to be used for him. Whether he’s pursuing this transition because he wants to be like his boyfriend, or whether he’s pursuing it for literally any other reason, it is no one’s place but his to decide what his gender is, and how he’s treated based on that.
Also, don’t use “female” as an ultimate gender marker based on what you’ve perceived a person’s “biological sex” to be. It doesn’t boil down to what a person was assigned at birth, in many cases, and I’m not okay with a cissexist standard like that.
I understand what your concerns are, and what the boyfriend of your former friend’s concerns are, but this really isn’t a decision either of you get to make, even if you strongly suspect that this person is being disingenuous. If it turns out he’s not a boy, he’ll figure that out soon enough, trust me, trans people have to go through a lot of gate-keeping before any severe and permanent medical changes are made.