Short answers, pulled from the story.
The first Army Group B emerged on the 12th of October 1939 under the leadership of Fedor von Bock. This command structure formed from the ashes of Army Group North after participating in the invasion of Poland.
Red Army counterattacks labeled Operation Uranus pierced defensive lines on the 21st of November 1942 and trapped the German 6th Army inside urban ruins west of the Volga. The command dissolved completely on the 9th of February 1943 following the Voronezh Kharkov offensive.
Erich Rommel assumed overall command of this formation which appeared on the 19th of July 1943 using personnel from previous iterations. His African campaign had recently ended decisively with the conclusion of the Tunisian campaign before he took charge.
Operation Market Garden began on the 17th of September 1944 and surprised the command structure while it defended the northern wing of the Western Front. Günther von Kluge assumed command on the 19th of July 1944 after Walter Model established his headquarters at Oosterbeek close to Arnhem.
The last remaining unit surrendered to the Allies on the 21st of April 1945 marking the end of over five years of continuous combat operations under various designations. Isolation in the Ruhr Pocket divided forces into smaller sections throughout early 1945 before total dissolution.