After you make sure that your NFA item is legal where you move to, both state level laws and any local ordinances, verify that your trust is still valid in that state if you went that route.
Normally you would use ATF Form 5320.20 for change of address on NFA items. It does not apply to suppressors, since your are not required to notify ATF. But they request that change of address information. If you chose to notify them of the new address you should use the 5320.20 for out of state moves.
I have several 22 suppressors in bound, a few Spectre II, Sparrow, Kodiak TL, Element II