Johnny,
Family researchers at http://www.rootsweb.ancestry.com/ and census records indicate George Henderson Conder survived the war.
His headstone photo in New Mexico is available at this site.
http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GScid=37948&GRid=7725474&
Military service records for George and his brothers are available at this site and also your Martin Conder's Confederate pension filed in Tennessee.
http://history-sites.com/research/index.html
Hope this helps,
Mitchell