Should be able to send to the service member’s unit at FPO or APO depending on if they’re in the army, navy, etc. This page www.usps.com/ship/apo-fpo-dpo.htm has more info.
You can absolutely receive mail and packages when deployed in the military, even during wartime. When I was in the USMC, getting mail while out in the field was a bit of a psychological life line.