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From Wikipedia
Iceland
Main article: Iceland during World War II
From 1918 until 1944 Iceland was self-governing, but the Danish King was Head of State of both Denmark and Iceland. As with the Faroe Islands, the United Kingdom occupied Iceland (to pre-empt a German occupation) but later turned it over to the United States, before that country entered the war in 1941. Iceland became a fully independent republic in 1944 and has remained so thereafter.
Greenland
See also: History of Greenland: Strategic Importance and History of Greenland during World War II
Regarding Greenland, on April 9, 1941, the Danish envoy (ambassador) to the United States, Henrik Kauffmann, signed a treaty with the U.S., authorising it to defend Greenland and construct military stations there. Kauffmann was supported in this decision by the Danish diplomats in the United States and the local authorities in Greenland. Signing this treaty “in the name of the King” was a clear violation of his diplomatic powers, but Kauffmann argued that he would not receive orders from an occupied Copenhagen.