Step 1: Analyzing the relationship.
- "My father's father" refers to the woman's grandfather.
- "The only daughter-in-law of my father's father" refers to her grandmother (because her grandmother is the wife of the woman's grandfather).
- "The only son of my grandmother" refers to the woman's father (since the woman's father is the only son of the grandmother).
Thus, the man in the photograph is the woman's brother.
Step 2: Conclusion.
The man in the photograph is the woman's brother.