or just do the best you can. some alters don't want stuff known about them yet. this stuff does take time. Maybe write little bits. only what feels ok. I know when T asked the same for me (also for assessment purposes), it put me/us in to a terrible state. But that's just me, not saying that will happen to you. But wanting you to feel you have options and that your rights matter. If you feel it isn't right, then don't do it.
I like the idea of writing with T - then she can direct you and say "yes I need this part, no I don't need that part".... best!