Was she relinquished for adoption as a baby? If so, does he know the name of the agency that handled it?

This is tricky. People are all so different, but as an adult adoptee, I would want to meet my birth father. I would probably be disappointed that he didn't take the initiative to search (given the fact that he knew the way her name appeared on her original birth cert) until he got terminally ill, but I would still rather meet him than not.

I agree with Chernabog, except that I would start with a fee based internet service, e.g., Intelius. It will be much cheaper than a human PI.