It depends on what he signed up for at the end. If he declined spousal support, she would have to have signed away her rights. My husband had to do that when I retired. There were a number of choices that could have been made at the time of retirement.
Below are two websites with more info but specifics depend on your Dad's final decisions:
Handles retirements and annuitants for Federal Government.
Deceased Annuitant Benefits
Page dealing with survivor (mother) of deceased annuitant (father).