William Henry Green married Rose A Phipps at Wellington, St Luke, Stoke on Trent.in 1913

There is a son born in Hanley, Stoke on Trent in 1914 William John Green ( Possibly your Jack)

Name: William J Green
Mother's Maiden Name: Phipps
Registration Year: 1914
Registration Quarter: Jul-Aug-Sep
Registration district: Stoke upon Trent
Parishes for this Registration District: View Ecclesiastical Parishes associated with this Registration District
Inferred County: Staffordshire
Volume: 6b
Page: 417

Image is where Ernest was born 47 Birch Street. (White door)