What changes if Britain takes control of the Azores on the assumption that they supported Germany during the Second World War?
Short answerThe premise is rejected: the Azores were Portuguese, and Portugal allowed British and American air operations through its alliance with Britain.
NotesThe Azores are distinguished from the Spanish Canary Islands, which may be the islands intended by the question. Portugal's longstanding alliance with Britain provided a diplomatic route to Allied air operations from the Azores. A submarine supply rendezvous near an island would not by itself establish a shore base. A functioning German base would require regular deliveries of fuel and other supplies through limited port facilities also serving the Allies. The argument therefore examines how such a base could be sustained as well as challenging the claim that one existed.