I have wanted to let a previous t or two know how i was doing now, so i understand the impulse. With one, i was also in a horrible relationship (not with the t) so that was part of it, to let him know "we" were fine (until we SO weren't!). The other t - i have actually consulted with a couple of times on issues with my current t, and that has shown me how now i am SO past him. I dont think he could keep up with me now. Maybe he could, but i have something different with current t. Maybe prev t is "better", but this works.

Eta - why a letter? Is he not taking your calls? Because i think just your tone on the phone, to him or his voicemail or his receptionist, would demonstrate the personal growth you have attained. Ie the first part of this last letter is enough, imo.