I'm assuming that you are filing a MA Form 1-PY/NR and as a part-year resident?
The insurance carrier need only show coverage for the period necessary as the part-year resident. Note the period as defined below.
This is the instruction from MA DOR
If you moved into Massachusetts during the year, the health care mandate applies to you beginning on the first day of the third full month following the month you became a resident of Massachusetts. For example, if you moved into Massachusetts on May 14, the mandate applies on August 1. If you moved out of Massachusetts during the year, the health care mandate applies to you up until the last day of the last full month you were a resident. For example, if you moved out of Massachusetts on July 10, the mandate applies up to June 30.
If you did not receive Form(s) MA 1099-HC, check the box to indicate you didn't receive a 1099-HC, and enter the name of your insurance company (or administrator) and your subscriber number.
This information should be on your insurance card.