In the 1901 census, Joseph Jr. (born about 1881) is living at home with Harriet, his mother noted as a widow. But in the 1891 census, Joseph Sr. is with Harriet, and Joseph Jr. is missing, altho' he was only ten years of age. Is Harriet a second wife who married Joseph Sr. after Anna's death, and Joseph Jr. did not come to join his father until he was settled in the UK?
Interestingly, Joseph Sr. and Harriet Edwards were not married until the quarter ending September 1894 in Chorlton, Lancashire. Getting a copy of the marriage record should provide the name of Joseph Sr.'s father and hopefully, a more exact place of birth.