There was no "official" notification process. His family might have gotten word directly from his company commander in a letter. A relative in the same company may have written. A neighbor, in a letter home, could have said "John Doe was killed in the battle last Friday, tell his family that he died facing the enemy." Some member of his company might have come home on leave and brought the sad tidings with him. As uncertain as things were then, I would think that a probate court would likely accept any of those messages as proof of death. Perhaps they required two separate confirmations, but that is conjecture on my part.