Formed during the One Year War by the survivors of Zeon attacks on Side 4 Moore, the group's main objective is to recover their destroyed homeland from the Living Dead Division. However, the Federation cares nothing about this goal and only views them as expendable soldiers.
The Moore Brotherhood fleet attempting to reclaim the Thunderbolt Sector was commanded by a ship called the Beehive, which appeared to have been a heavily modified Columbus-class, while the headquarters, located elsewhere, was responsible for providing reinforcements and funding the development of mobile suits.
During the battle with Zeon's Living Dead Division, the Moore Brotherhood suffered heavy casualties. However, the situation began to turn when it received the FA-78 Full Armor Gundam (Thunderbolt Ver.).
Piloted by Io Fleming, the Full Armor Gundam scored many victories against the Zeon forces, forcing them to deploy the still experimental MS-06R Zaku II High Mobility Type (Reuse "P" Device) (or "Psycho Zaku" for short) in response.
In the end, the Moore Brotherhood fleet, including the Beehive, was destroyed by the Psycho Zaku, which went on to defeat the Full Armor Gundam. Most of the group's surviving members surrendered to Zeon reinforcements after a failed attempt to capture the Living Dead Division mothership Dried Fish. These survivors were later freed by Io Fleming and escaped after the ship transporting them crashed.
In the manga, the Moore Brotherhood emblem can be seen on the rebuilding Side 4 colonies. It is unclear if the emblem was the original Side 4 emblem or if the rebuilt Side 4 used the Moore Brotherhood emblem to honor them.