In order to qualify for the MA moving expense deduction, the move must relate to employment or business income that is subject to Massachusetts tax. Since your moves relates to a new job in another state in which your income will not be subject to MA taxation, you do not qualify to take the deduction.
https://www.mass.gov/info-details/moving-expense-deduction
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
