I did an SBR on a trust here in Georgia, and I have recently just moved (still in the state of GA).  How do I go about changing my address with the BATF?  Can I do it on paper and mail it in with my next application for a tax stamp?  I am about to purchase a can, can I just assign the suppressor to the same trust I have the SBR assigned to?

bump, i need an answer if possible

Caveat:I'm a newbie at NFA stuff.

I think you just use a 5320.20 (same as for interstate transportation of NFA Title II firearms),but select "no" for question#2 ("Firearms to be returned to original location?").

The fact that they're not being returned indicates a permanent move.

For your trust, your second set of paperwork would simply indicate your new address for the trust. So the new suppressor would be Form 4'd under the new trust address, and you'd use a 5320.20 to change the address of the existing SBR already on the trust.
You'd add the suppressor to your assets list for the trust of course (along with the already present SBR).