We checked to see if his wife Mary applied for a pension; she didn't. She remarried in 1871; no record of her and AJ divorcing, which leads me to believe he simply left the region or died in the Civil War. No record of him applying for pension either.
The record of the AJ Cooper in the 42nd who I think lived in Walton County says that he went to Cusseta, Al. after the war. However, there is a Cusseta, Georgia also down near Columbus and the Alabama reference could be an error. I will check on these two towns with the same name and see if there is a record of him living there and/or being buried there.
Thanks for your interest in AJ. He is our "brick wall" -- the ancestor we can't find; he might be the 42nd AJ or a dozen others -- Andrew Jackson was a common name in that era.