I read the information given and Mr. Simmons is, I believe, incorrect. The date of death was given as...
"I can not tell you the day of the month he died but it was during the first part of August."
Since the letter was written in May of 1864, that would have to have been the year 1863, or about two and half months after the Battle of Champion's Hill and about one month after the fall of Vicksburg. I would think the parole camp was still there at that time.
David