Source: US UK intervention.org
End of the Italian colonization of Libya, when the Sanussiys give in. 
With the fall of the Axis powers in the World War 2, Britain and France divides Libya: Tripolitania and Cyrenaica comes under British control. Fezzan comes under French control. 
In secret talks with the British, U.S. officials agree to support a British base in Cyrenaica and also agree, as the best way of securing this base, to a British trusteeship over that province.