There is no record for a 13th Battalion, Virginia Cavalry

39th Battalion, Virginia Cavalry
Organized: on 9/24/64 Mustered Out: 4/9/65
Scouts, Guides & Couriers

John H. Richardson, Major, 39th Battalion Virginia Cavalry, appointed September 24, 1862,

The 39th Battalion Virginia Cavalry consisted of four companies, A to D, which had been organized on various dates from August 18, 1862, to January 26, 2864. It was also known as the 13th Battalion Virginia Cavalry and as Richardson’s Battalion of Scouts, Guides and Couriers

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39th Battalion, Virginia Cavalry
OVERVIEW:
39th Cavalry Battalion [also called Richardson's Battalion of Scouts, Guides, and Couriers] was organized with two companies, later increased to four. It was attached to General Headquarters, Army of Northern Virginia, and served as General R.E. Lee's personal cavalry command. The unit participated in every engagement at which General Lee was present from Fredericksburg to Appomattox. On April 9, 1865, it contained 1 officer and 80 men. Major John H. Richardson was in command.
https://www.nps.gov/civilwar/search-battle-units-detail.htm?battleUnitCode=CVA0039BC

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See this old thread:

http://www.history-sites.com/cgi-bin/bbs62x/vacwmb/webbbs_config.pl?md=read;id=6792