Ann, therapists have all different kinds of views on communication between clients and therapists.
Without knowing your previous therapist, I couldn't say with certainty how she'd react to you sending her a letter. But, what I can tell you is that in general, therapists very much are interested in how people are doing- after people leave therapy for whatever reason we don't usually get to know how they do, and that's hard!
So, I think in this case it's fine for you to write the kind of letter you are suggesting. When you write her, be clear about how you are conceptualizing the letter (just say exactly what you did in your comment- that you don't expect her to write back, that you know you guys didn't talk before she left about communicating, and that you felt you really wanted to let he know how the transition had gone for you and how you are doing now). When you're clear about the conceptualization of the letter (what you expect, how you'd want her to respond, etc.) it is so helpful for the therapist- it lets us know what you're thinking, what you want- helps us not accidentally disappoint or surprise you by doing something you didn't expect or intend.
I actually think this letter of yours is nice on several levels. It not only allows you to to tell her how you're doing, she also gets to know that you've made it through the transition and that although it was a challenge you are ok, and it allows you to acknowledge the work that you and she did (and it was a significant, and successful, piece of work you two did, for sure!).
So, as far as I can see, go for it!