Menken's rifle was a gun wielded by various characters on Gaman's moon.
The rifle was one of two given to the Sapaar guards protecting the shuttlecraft in the playhouse. Werner unarmed and incapacitated them while stealing the ship and escaping Gaman's destruction with a group of Union survivors.
Later, when Werner and his followers settled on Gaman's moon, the two rifles and some hunting pistols were their primary source of protection to dissuade the nearby Sapaar camp from ambushing them. One night, the Sapaar attacked after a celebration, and only Menken was able to hold onto his rifle. All other weapons were stolen.
During the construction of the Einstein-Rosen Bridge, a guard was posted every night with the rifle to guard the bridge. Kixoo was this man the night before the bridge was to be turned on, but he was attacked by Brut, who stole the rifle and used it to puncture the fuel canister that would have powered the bridge.
Werner tracked Brut into the mountains and discovered the gun, abandoned and out of ammunition. He carried it with him to Brut's cave, but lost it in the scuffle that claimed Brut's life. (Ship of State)
Menken discovered the rifle after both camps hid in Brut's cave from the tropical storm. He owned it for years, and finally wielded it after gathering a posse to force Trano and the Sapaar to stop defending the brewery. Luckily, the situation was resolved peacefully. (Next of Kin)