Death certificates are a wonderful source, but usually the decedent does not provide the information. Is there another form or record where the deceased would have provided the information? One such source in the United States (for recent enough individuals) is the SS5 form--Application for a Social Security Number. The current charge is $27, but in some situations, knowing who the person actually listed as their parents may be helpful. A copy of an SS5 form from 1943 is here.