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Your question was answered. You need a MA machine gun license to possess a MG in MA.
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And from my very basic research into this in the past, I believe you need to either have a police certification or be a "recognized collector", i.e. have a C&R FFL. And thats all for the resident MG licence. There is a non-resident "licence to carry" you can apply for, but I don't think there is a non-resident MG licence.
Remember, the 5320.20 form is a federal form that keeps you in line with the federal requirement to seek approval to cross state lines. Even if you have that, you still need to abide by all the laws and requirements of the destination state. You may be better served asking for specifics in the MA hometown forum, or maybe contacting the MA state police for guidance.