The unit name is 15th Confederate, not 15th Alabama. Also, its 'Cavalry', not Calvary.
H A Ball of Co "E", 17th Mississippi Cavalry Battalion joined Capt Steede's Company Mar 1, 1862. The battalion became part of the 9th Mississippi Cavalry when that command organized. He is absent without leave on roll with Co "A", 9th Mississippi Cavalry during Nov - Dec 1864. He appears as a member of that command when he received a parole at Mobile AL May 23, 1865.
If H A Ball and H C Ball are the same person (and both are reported as residents of Green County MS), then this man joined Steede's Company and served under that officer during 1862 and 1863. At some point in 1864 he deserted that company and joined Co A, 15th Confederate Cavalry. We cannot say how or exactly when that happened. H A Ball was last paid in this command on Oct 31, 1863. When General Taylor surrendered all Confederate forces in the Department of Mississippi, Alabama and East Louisiana, Ball must have gone to Mobile. I cannot explain how or why he would have received paroles on consecutive days in late May 1865.