For MA:
You need to notify Issuing Authority and FRB by Certified Mail ONLY (suggest Return Receipts as well) within 30 days of your move.
There is no such thing as changing a Resident LTC to a NR LTC. You need to apply to Chelsea for the NR LTC, they will schedule an interview and based on what you tell them your specific needs are, a 1 year NR LTC will be issued with or without restrictions.
For NH:
Enjoy the freedom!
NO permits of any kind needed to own anything!
NH LTC is needed ONLY to conceal carry or carry loaded in a MV. Cost is $10 and done thru your local PD, no pictures and no prints required and they have 14 days to issue it.
Good luck!