This,unless it is ITAR items there should be no issue.You only have to provide normal, domestic postage on mail going to an APO or FPO address.
The United States Post Office delivers APO and FPO mail to a military port, located on the East Coast or West Coast of the United States (depending on where the member is stationed/deployed), and the military takes over from there, transporting the mail via military cargo aircraft to the overseas location/Navy ship.