This sounds like he was with Jubal Early in front of Washington, DC, July 11, 1864 where Pres. Lincoln peered over Confederate lines at Fort Stevens.
Hart's battery is not listed with Early's troops at this time.
Robert Anderson Webb, Private, Capt. Hurt's Company, Alabama Vols., McIntosh's Battalion, Light Artillery, enlisted October 22, 1863 in Bibb County, Alabama by D. O. Baird for the war, in arrest January, 1864, subject of Court Martial March 26, 1864, on detached service the end of 1864, building Chevaux de flaire, paroled at Appomattox Court House, Va. April 9, 1865, signed parol document at Montgomery, Ala. June 7, 1865 with his mark, 'X', description, 5' 11", light hair, blue eyes, fair complexion
M311: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Alabama