The two links I listed are both him: Henry listed his service 1864-65 in 45th Inf in the 1890 Moniteau Co census schedule, and Co C of 45th was transferred to the 50th:

45th Regiment Infantry

Organized at Sedalia, Warrensburg and Otterville August 10 to September 17, 1864. Attached to District of St. Louis, Mo., Dept. of Missouri, to December, 1864. Unattached, 4th Division, 23rd Army Corps, Army Ohio, to March, 1865.

SERVICE.--Moved from Warrensburg, Mo., to Jefferson City, Mo., October 1, 1864. Price's attack on Jefferson City October 7. Duty at Jefferson City until December. Moved to Nashville, Tenn. Battle of Nashville December 15-16. Garrison and guard duty at Spring Hill, Tenn., until January 5, 1865. Moved to Johnsonville,Tenn., January 5-13, and duty there until February 20. Moved to St. Louis, Mo. Mustered out March 6, 1865. Companies "C" and "D" transferred to 50th Missouri Infantry and Companies "G" and "H" to 48th Missouri Infantry.
Regiment lost during service 4 Enlisted men killed and mortally wounded and 82 Enlisted men by disease. Total 86.