Shule’s throne is the throne in Shule’s own kingdom upon which his sons placed him after freeing him from prison. The sons of Shule “crept into the house of Noah by night” and slew Noah as he was about to put Shule to death (Ether 7:18).
Shule’s sons broke down the prison door, brought out their father, and “placed him upon his throne in his own kingdom” (Ether 7:18).