Prior to independence in 1975, Surinam was a colony of the Kingdom of the Netherlands with no government of its own. A Governor General was appointed by the Dutch crown (in practice the Department of Overseas Territories), who co-governed with the assistance of the 15 member Estates of Surinam elected by the colonial elite.
With the establishment of the Dutch Government in Exile under Queen Wilhelmina, both Dutch Guyana and Dutch East Indies (ie the future Indonesia) were administered as before evacuation of that government to London.
After the establishment of the Vichy government in unconquered France, Wilhelmina took the action of replacing her Prime Minister, Dirk Jan de Geer, with Pieter Sjoerds Gerbrandy due to the defeatism of the former. All Dutch Colonies were administered by the eponymous department headed by the Minister of Colonies, a position also held by Gerbrandy in the Government in Exile.
The timeline suggests that recognition of jurisdiction over Surinam by the Dutch Government in Exile, even through the American occupation of the colony for most of the war, was de facto in exchange for that body signing the Atlantic Charter, under which the signing colonial powers agreed to end colonial relations with their colonies post-war.