I have contacted previous T's with updates. The one that I have contected the most (3 times over 15 years) had invited the updates at the time of our termination.
I think if your old T mentioned appreciating the update, then I don't see why you can't send another one. It doesn't come off as stalking to me; it's simply updating. I think most T's are ok with that, espesically with the understanding that no response is needed/wanted.