Believe you’ve misread this note in your query:
“ . . . Interestingly, his next letter dated Jan. 2, 1865, was from "Genl. Hospital, Greenville," but there is no indication if he was sick or wounded. ‘“
Your attachment contains this note which indicates the writer was not from him.
“ . . there are also two letters addressed to Fleming. One is a note from I. B. Hugghins who was in a hospital in Greenville, Ala.”