Pointing to a man in the photograph a woman said, "He is the son of my paternal grandmother's only son. How is the man related to the woman?

Brother

Let's analyze the statement step by step.

"He is the son of my paternal grandmother's only son."

1. My paternal grandmother = My father's mother.
2. My paternal grandmother's only son = My father.
3. The son of my father = My brother (or myself if the speaker is male).

Since the speaker is a woman, the man in the photograph cannot be herself. Therefore, he is her brother.