Concept:
Family relation problems often involve interpreting statements carefully to identify relationships between individuals.
Step 1: Analyze the statement.
The woman says:
\[
\text{"His mother is the only daughter of my mother."}
\]
Step 2: Interpret the phrase.
The phrase "only daughter of my mother" means the woman herself, since she is the only daughter of her mother.
Step 3: Substitute the meaning.
Thus, the statement becomes:
\[
\text{"His mother is me."}
\]
Therefore, the woman is the mother of the man.
\[
\boxed{\text{Mother}}
\]