for grad school tuition, once you've been declared instate or out of state tuition, is there any way they can tell if you moved or not?

Read the fine print on your FAFSA - providing false or misleading statements on your financial aid applications can expose you to a $20,000 fine, or prison, or both. Also, providing incorrect information on a student loan promissory note and not keeping your loan servicer up to date on your address might cause you problems down the road. MOST institutions of higher education have a policy about false and misleading statements - your grad school might merrily take your money, but, lie to them & they will NOT release your transcript or award your degree until you've paid up!

If you don’t mind strangers seeing your grades or taking your check, then no.

Aren’t your transcript sent to your home.