A states that his mother is the only daughter of B's mother.
This means B's mother has only one daughter, and that daughter is A's mother.
Since B's mother has only one daughter (who is A's mother), B cannot be a daughter.
Therefore, B must be a son of B's mother.
B is the son of B's mother, while A's mother is the daughter of B's mother.
This makes B and A's mother siblings (brother and sister).
Since B is the brother of A's mother:
B is A's maternal uncle.
Therefore, the answer is Option 3: Maternal Uncle.