This Joseph seems to be definitely the son of the son of Juda Ashkenazi son of Simon

http://akevoth.org/genealogy/ashkenazi/11374.htm shows Joseph together with Bele Isaac Frankfort, birth had a son Juda Joseph Frankfort, birth Jan 1776 Amsterdam, 'Circumcisions and Births in Amsterdam 1697-1811, by Jits v.Straten':
in Teveth 5536 - birth of Juda ben Joseph ben mhor"r Juda F"F
on 9 Teveth 1776 - circumcision of Juda Judale ben Joseph F"F-Toktin