Linda, most of the men of the 36th and 37th Arkansas Regiments captured at Helena were sent to Alton, Illinois, and later sent to Fort Delaware, where they were held until March 1865, when they were forwarded to City Point, Virginia, for exchange. Officers, of course, were sent to Johnson's Island, near Sandusky, Ohio.
If I remember correctly, the "Solomon" you referred to is Pvt. Solomon R. Moore, Co. A, 36th Arkansas Regiment. He was captured at Helena, confined at Alton, and exchanged at City Point on March 7, 1865. He was admitted to a military hospital at Richmond, Virginia, and was left there when the city was evacuated in April. A U.S. Army report for the month of May 1865, which listed Confederate soldiers captured in various Richmond hospitals, included Pvt. Solomon Moore. There is no further record of him. Presumably, he died in the hospital.