As long as you are a MA resident there are only two legal processes available to you.
1. You get his mother to send a notarized letter stating that as the executrix of his father's estate, the gun (with appropriate Make/Model/Serial number) is left to him.
Then your hubby goes to the local PD and gets the paperwork to apply for a Lic. to Carry (which is required to own/possess any handgun in MA) and he fills out the paperwork and pays his $100 and then he waits and hopes the local Chief of Police approves it. If it gets approved he picks up his LTC.
Then he goes to the MA State Police WWW site and downloads a copy of the firearms registration paperwork and fills that out and attaches a copy of the notarized Estate paperwork and you send that to the State Police and hope they accept it.
Provided he gets a LTC and the State Police accept the registration he can now legally own/possess the handgun and he can legally sell it to either a used firearms dealer or another private party as long as they also have a proper LTC.
or....
2. You hide it and hope Boston has another "Turn in a gun and get a gift card!" amnesty promotion and quietly show up at any Boston Police Dept office and turn it over. In return, they'll give you a $25 gift card to Target. (which somehow just seems like the appropriate store...
)
Are you still planning on moving out of state? If so I'd just hold onto it and sell it there (unless you happen to be moving to IL or Hawaii)
btw, MA requires that it be stored in a container approved by the State and it can't be stored in a shed or vehicle.