If a woman says "His mother is the only daughter of my mother" while pointing to a man, then the woman is the man's mother.
Explanation
The woman is referring to herself as the only daughter of her mother.
"His mother" refers to the mother of the man she is pointing to.
Since the woman is the only daughter of her mother, she is saying that "his mother" is actually herself.
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So, the woman is the mother of the man.