My understanding of the Mass rules is that you can only carry forward a capital loss incurred while you were a resident of Massachusetts. So if you realized the capital loss prior to moving to Mass, you might not be able to use that loss to offset this year's capital gain on your Mass return.

Did you try to find this answer on the Mass Department of Revenue's site?

Zip Code: 01801

I cannot not seem to find any information that directly addresses this problem. However, would it not be a big penalty to moving if you cannot utilize prior carry-over capital losses for state taxes just because you moved?