Your ancestor, H. J. Williams, died in prison at Camp Douglas and is buried at Chicago IL. I will provide more on that shortly.
Another post to your inquiry identifies the H. J. Williams at Oakwood-Montgomery AL as being a member of the 25th Alabama.
Your ancestor was a member of Co. "B", 2nd Battalion, Hilliard's Alabama Legion. He was captured during the hand-to-hand fighting on Snodgrass Hill which ended the Battle of Chickamauga GA, Sept. 20, 1863. Williams' company commander, Capt. West D. Walden, was seriously wounded here.
All this occured before the 59th Alabama Regiment organized on Nov. 25, 1863. Williams' name was retained on roll because no one serving with his company knew that he had been captured. Eventually they concluded that he must have been killed at Chickamauga.
Federal prisoner of war records show that H. J. Williams died of typhoid fever on Nov. 1, 1863 at Camp Douglas, Chicago IL. He was buried in Chicago City Cemetery in grave no. 789. These are included with Williams' service record with Co. "B", 2nd Battn., Hilliard's Alabama Legion.