Combined information from TX Dth Idx Online, and SSDI:King G. Peters b 10 Feb 1896, d 12-23-1974, last residence Houston, Harris Co, TX, and SS card issued in TX.
Henry William Peters b 21 Feb 1895, d 4-20-1983 last residence Dallas, Dallas Co, TX, and SS card issued in TX.
The William Henry, and William H. Peters, did not make a match either in year of death, birthdate (way off from King Peters') or location of death.
You might have trouble obtaining copy of death certificate of W.H. Peters unless you can prove direct relationship.I think there is a 25 year restriction on deaths.Try Dallas Co, TX GenWeb site, post a query, see if you can get someone to go take a look at the death record and find out who was the informant?Or, check for obituary, survivors might be listed.Contact Dallas Public Library, they have great genealogy department, should have website listed on the Dallas Co, TX GenWeb site.They would probably check for obit for you, since you have exact death date.