Is the firearm C&R eligible? If not, you definitely need to go through an 01 FFL. I believe it will have to be an NH FFL. This is definitely true for a handgun due to federal law. IIRC there's also a law that prohibits a MA FFL from selling a gun to a non-resident.
According to c140 s128A, you can only sell a gun to either a dealer, a museum, or a MA resident with an FID/LTC. So, while in MA, you cannot sell a gun to an out of state C&R. However, if the sale takes place in NH, then NH law applies.
If I was trying to buy a C&R from a seller in MA who wanted to fill out a FA-10 and include my name/addr on it, that would be a deal breaker for me to buy it.
If I was trying to buy a C&R from a seller in MA who wanted to fill out a FA-10 and include my name/addr on it, that would be a deal breaker for me to buy it.
Slight clarification, an FA10 is not used for any out of state transfers simply because nobody who needs to fill out an FA10 in the first place is allowed to conduct an out of state transfer. Transfers into the state may indeed require an FA10, per c140 s128B.