I don't see Elizabeth b 1779, Greasley in the tree you have posted.
However there is a death in 1844 - Elizabeth Birkin 65 yrs in Basford district.
That is the Elizabeth Birkin I mentioned in reply 26
This is Thomas & Elizabeth Birkin on the 1841 census
1841 England, Wales & Scotland Census
Toll Bar, Kimberley in the parish of Greasley,
Piece 857 / Folio 29 / Page 5
Thomas BIRKIN, aged 63 - Grocer - born in county
Elizabeth BIRKIN, aged 62 - born in county
Next door is their son Thomas Birkin (Lace Maker) and his wife Susannah nee' Walker - married in Greasley 1836
Elizabeth's burial is given in reply 26
Burial at Greasley - abode Kimberley
14th Nov 1845, Thomas BIRKIN aged 67
Thomas Birkin also left a Will - granted 1846
The couple also have other children - even if these aren't people that you are interested in, it is always useful to cross reference information if only to rule them in or out.
As I haven't had any feedback either way I will leave the thread, at least for now.