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Thanks for your question. If the boys father was born out of the UK then I am afraid he is not eligible for a British passport. Citizenship by decent can only be passed one generation. As the boy's father was born in Rio he would have been a British citizen by descent not by birth ( which requires birth here) In order to be entitled to a British passport his father would have to have been born in the UK ( or his mother ).
I am sorry if that is not the answer you wanted but he has no right to a British passport and could only acquire one by residence in the UK the same as any other foreign national. His English ancestry give him no extra citizenship rights.