Q. How do I prove to NYS taxation so that I do not owe taxes to them post August salary?

A. You don't try to prove anything at tax filing time. You wait to see if you get questioned, after filing your part year resident NY return.  The most important thing is to get your employer to stop withholding NY tax effective the date of the move. It's when your state return asks for the refund of mistaken withholding that the NYS taxation people wonder why.