According to book "In the Saddle With the Texans--Day by Day with Parsons's Brigade 1862-1865" Company K was only a attached to Morgan for 2 days before end of war . In another book,"Texas Confederate Deaths In Union Hospitals & Prisons",there are 2 J Cox listed(Jas.M Cox & Joseph Cox)as dieing at Camp Douglas and both were buried in what is known as "CSA Mound" located at Camp Douglas. The Jas. M. Cox was from Co. G--17th Infantry,died 27 March 1863 and Joseph Cox was from Co. K-18 Cavalry,died Feb. 07,1863. You could probably find their prison records at National Archives but they probably won't list any more information than what I have told you. I had same problem with my grt-grt-grdfather that never returned from war after being captured at Arkansas Post(Fort Hindman). Hope this helps some!!