Absolutely be honest. I am not sure if that was the question.
The last time I filed in Massachusetts, they made you wait for some time before you received any benefits... and the waiting period didn't start until you filed your first claim (which you wouldn't get anyway).
So, just follow the instructions. If there is a "last day of employment" field, then file the form with the correct information. That is what I would do. I am pretty sure they will figure it out and won't pay you any more than you are owed.