There isn't a MA law, but there is a CA one that prohibits people from shipping anything regulated to any FFL there without first becoming a CA approved "distributor" (it may have been listed as "approved dealer", etc
, or some such BS. As I read the laws there, the way to do it will require 2 FFLs, not one. You can't ship to his CA FFL as I understand it. You can ship to a CA approved distributor who then ships to CA. You can find a CA approved source FFL/distributor by trolling gun broker for the term "will ship to CA". You ship to them, they ship to the CA dealer.
BTW: The whole point of this insanity from what I can tell is they think the FFLs in CA are selling guns outside of the CA registration system and want the out of state dists/dealers to file a separate form with the CA-DOJ with the number shipped in so they can compare those, with sales and inventory and find "missing" guns.
ETA: You may want to post this question on CalGuns. They will know the CA law better than anyone.