I have found conflicting reports of his death. The Rootsweb and Ancestry.com connections I have made show his death in 1862. I found him still alive in 1865 (according to the Footnote 43rd Regiment records) and I was told by another mscwmb contributor that he was hospitalized at West Point in 1865 with typhoid.
The following was found on Rootsweb: "Henry developed Typhoid Fever during the war, was on his way home and made it to his father in law's house before he died."
Entry 8862 by MaryBeth
All entries that I have found seem to agree that he is buried at the Anderson Family Cemetery, Fearns Springs, Winston County, Mississippi.
There is a photo of Anderson and his wife, Margaret Reed Holmes Anderson, on Ancestry.com.
I hope this is helpful.
Sara