Both can use the box.
Although I wouldn't use a po box at the govt building.
I would use a private service. It is a matter of how each is addressed... The living soul might use upper lower case, C/O in front of the mailing location, brackets or a box around the zip code... Fictions use the ALL CAPS name, may not need C/O or brackets around the zip code. One may sign as agent without recourse if you are signing for the fiction as well. or agent w/o recourse for: ALL CAPS NAME.. or Trustee if you are acting as the trustee for the all caps name.
I prefer Heir/Beneficiary.. my preference.
use separate addresses for each party to create the clearest separation between the parties.