Our James Chambers Williams, Jr. (Jim) was the son of Ella Alabama Greening Williams, who was married to James Chambers Williams, Sr. This son was my husband's father. He married Mary Thelma Robertson, and they had twelve children. My husband was born in 1938, third from last child.
Your Jim might have been kin to the other Williams, from DeSoto Parish, La, who were also kind, in some way to the Greenings, but I don't know anything much about them.
Sorry to be of so little help. Melba