IANAL, but my understanding leads me to disagree with the trend of this thread.
1) There is a 60 day grace period for people moving into the state to legally posses firearms in the state of MA. (see:
http://www.goal.org/PDF/newres.pdf, I don't have the MGL reference). They can possess in the home, but not transport or carry.
2) Buying from folks without an LTC/FID has been covered here before (see:
http://northeastshooters.com/vbulletin/showthread.php?t=8677&highlight=transfer) and I'm inclined to believe it is correct. Check with a lawyer, but a very qualified one gives his stamp of approval in the referenced thread.
So, 1+2=you get your gun. If they bring more guns than just that one, they will have to sell them (without transporting them) within 60days. If they are not on EOPS, then the sales will have to be FTF, not to or through a dealer.
Matt