I'm not going to pretend to actually know the law in the case of moving them off to another state.
HOWEVER, I recall reading one story (might be here on NES, might have been elsewhere) where someone's permit was yanked (don't recall if it was a 209A or just a "suitability" revocation). The PD shows up to confiscate everything and no guns! He tells them that he moved them to a NH location and the MA local PD contacts the NH local PD (seem to think it was Manchester, but not certain) and the NH PD confiscates the guns for the MA PD!
This might be where having a good lawyer can be helpful. I know more than a few people with homes in VT, NH, ME as well as MA. If the PD knows this info they will try their best to confiscate your stuff and sister PDs in other states may well be sent to do their bidding.
So best advice is consult with a lawyer long before you have a "need" and then have a "plan" to secure your goods in a legal manner in another state to protect your assets. Of course this all assumes that the issue does NOT involve someone who has become a "federally prohibited" person . . . that any issues are "local" (MA) in nature.
How did the Mass PD demand to know where in NH they were located? What if he decided not to answer that question?