I'm curious as to where you have looked for information. The officer's military service file includes fifty-five images and should have been your first stop. These show that he died at Montgomery Hospital, White Sulphur Springs VA. At the time of death he was carrying $360.75. Cause of death is not listed, but must have been disease. In addition ADAH has the original roll kept by the orderly sergeant, turned over to the ADAH by Capt H H Sartain. This roll gives Conner's age, occupation and physical description, plus date and place of death.
At the time of Conner's death, the 41st Alabama Regiment was in transit from camp in East Tennessee to Petersburg VA.