As I understnad it, Company A, of Crawfords Cav, most likey refers to a Battalion commanded by Lieutenant Colonel William A Crawford that was made up of two companies that were excess conscripts from the 19th and 24th Arkansas Infantry Regiments.

Company A, Commanded by Captain Joseph J. Ingram, organized at Pine Bluff, Arkansas on June 23, 1862.

Company B, Commanded by Captain L. A. Weatherford, organized at Eagle Creek, Arkansas on July 15, 1862.

Neither of which have a obvious connection to Solomon I. Brandenburg, of Desha County.....