I thought I'd post this much while I have it. I haven't connected the dots on Fannie's marriage or looked for Edith or the parents.
-- Edith was born in RI - there is a Warwick,
Rhode Island, as well as the one in England, and the next column on the 1875 Census was "parentage" not place of birth. It doesn't look like their son Joseph came to the US, or Joseph's son William.
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SMITH, SARAH mmn: GREENWOOD
GRO Reference: 1855 J Quarter in MANCHESTER Volume 08D Page 318
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1861 Census Stockport
44 Hollins Fold
Joseph 39, born Lancashire, Heaton Norris, occ: a [something or other] cotton spinner
Jane 29, b Manchester, occupation: card woven hand ?
Sarah 5, b Lancashire, Beswick
Jane 8m, b Cheshire, Marple
Joseph 2, b Derbyshire, Charlesworth
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1885 RI Census, North Smithfield
June 1, 1885
for some reason, the images are of an index of sorts, I think. but at least in alphabetical order of first letter of surname. Males separate from female. The district number and family number tie the family together:
District Number, Family Number, # people in Family
image 44
151, 31, 6
Joseph Smith, head, born in England, no occupation, alien
image 98
151, 31, 6
Jane Smith, wife, 50, born in England, cotton weaver
Fannie Smith, daughter, 20, born in England, cotton weaver
Sarah Smith, daughter, 28, born in England, cotton weaver
image 99
151, 31, 6, Edith R Smith, daughter, 12, born in Smithfield, parentage: Eng, 10 months in school
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Record of a death, State of RI
March 26, 1930
Fannie Sharp, born October 26, 1872, England
died at Westerly Hospital, RI
usual residence: Pendleton Hill Road, Stonington, CT
married, housekeeper, husband: George W Sharp
parents: Joseph Smith, Jane Greenwood, both born in England
buried: River Bend Cemetery, Westerly RI
informant: George W Sharp, husband
https://www.familysearch.org/ark:/61903/1:1:F8HM-DW5------------
Certificate of Death, RI
Sarah Smith
June 27, 1941
at 15 Main Street, White Rock, Westerly
white, female, single, born May 21, 1865, Manchester, England
father: Joseph Smith, born in Stockport, England
mother: Jane Greenwood, born in Manchester, England
informant: Mrs Edith Gildea, sister, same address
buried: River Bend Cemetery, Westerly
https://www.familysearch.org/ark:/61903/1:1:F8H5-MX9