No. Moving expenses are only deductible on a federal return for certain active duty members of the military.
https://ttlc.intuit.com/questions/4482873-which-federal-tax-deductions-have-been-suspended-by-tax-re...
Some state laws about moving expenses are different--but YOU did not move. Your son moved. What you paid for his move was a gift, which is not deductible. He might be able to use moving expenses on his own state return.
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**
