Short answer
After living legally in the Azores for the required period (historically five years, but rules are under review), you may apply for Portuguese citizenship by naturalisation. You will need to demonstrate basic Portuguese and provide documentation. Confirm current requirements with the Portuguese Ministry of Justice or a legal advisor, as rules change.
General information, not legal or tax advice. Rules and amounts change: confirm with official sources.
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A renovated 5-bedroom house in Ribeira Grande, São Miguel island, minutes from the beach and local life.