Personally, I would get a marker I could afford and place it there in his memory.
There are a lot of affordable websites - we did this at a grandmother's site as the
grandfather's grave cannot be found - so when it is found we can move the marker.
It's on legs and at least his name and years are recorded. We did contact the caretaker and he said even people buried at sea have a marker In the cemetery. Luck to you.