Both Mayflower Families and Great Migration indicate that Elizabeth Fuller who married Moses Rowley was the daughter of Matthew Fuller of Mayflower line (i.e, Edward Fuller of Mayflower was his father).
References [
https://www.americanancestors.org/databases/mayflower-families-fifth-generation-descendants-1700-1880/image/?volumeId=48512&pageName=104&rId=1415598249 ''Mayflower Families Fifth Generation Descendants, 1700-1880'']. (Online database: AmericanAncestors.org, New England Historic Genealogical Society, 2017). From Mayflower Families Through Five Generations: Descendants of the Pilgrims who landed at Plymouth, Mass., December 1620. Plymouth, MA: General Society of Mayflower Descendants, 1975-. Reference Edward Fuller Volume, page 104 Mayflower Families 4:10-12 also has this information.
This is from Great Migration Begins:
[
https://www.americanancestors.org/databases/great-migration-begins-immigrants-to-ne-1620-1633-vols-i-iii/image/?volumeId=12107&pageName=1603&rId=1415519586 ''The Great Migration Begins: Immigrants to New England 1620-1633'', Volumes I-III]. (Online database: AmericanAncestors.org, New England Historic Genealogical Society, 2010), (Originally Published as: New England Historic Genealogical Society. Robert Charles Anderson, The Great Migration Begins: Immigrants to New England 1620-1633, Volumes I-III, 3 vols., 1995). Page 1603
This source shows that Matthew (son of Edward) married Frances ______. [
https://www.americanancestors.org/databases/great-migration-begins-immigrants-to-ne-1620-1633-vols-i-iii/image/?volumeId=12107&pageName=712&rId=1415513146 ''The Great Migration Begins: Immigrants to New England 1620-1633'', Volumes I-III]. (Online database: AmericanAncestors.org, New England Historic Genealogical Society, 2010), (Originally Published as: New England Historic Genealogical Society. Robert Charles Anderson, The Great Migration Begins: Immigrants to New England 1620-1633, Volumes I-III, 3 vols., 1995). Reference page 712.
Here is another source that shows Matthew married Frances _____, and that his daughter, Elizabeth married Moses Rowley: TAG 61:198-99
Does this information provide sufficient information to show that the granddaughter of Edward Rowley is the one that married Moses Rowley, and that she is the daughter of Matthew, granddaughter of Edward?
I will add all these sources to her profile.