Your friend needs to talk to his father (if he's still alive and in the picture) or family members on his mother's side. If there are none, then he needs to speak with anyone at their wedding. If none, then expand the search to anyone who knew them as a couple, at any time.
Ask these people: did she ever talk about family or where she was from or how and where she and the father met? These will provide clues as to where to look in Vietnam.
If none of these people can be found, then the next step is the consulate for your country in Vietnam. Give them every clue.
Prepare for this to take money and years. The less information you have, and the more remote the connection, the more expensive and longer it will take--- if it can ever be successful.
And BTW if the consulate is no help then the final step is taking photos, going to Vietnam with an interpreter if you need one, and manually checking records that have only a slim chance of having been scanned. I hope you like boring slogs through big, dusty old books, because it may come down to that.