See posting of the Tecklenburg Borgmans on this listing for some of the St. Louis Borgman family descended from George Heinrich Borgman (aka Joergen Heinrich B.) It is possible that one of the four son's downlines could be tied to your Frederick Wilhelm.
My line from Johann F. Borgmann has children circa 1864/1866in the Cappeln, St Charles Co, MO area.Johann was b. in Germany 1830.
The family has found christening records in the German Evangelical Churchbook of St. John United Church of Christ, Cappeln, St Charles Co., MO.The sponsor is listed as "farmer, Johann Henrich Borgmann of Cappeln" and father information is Georg Henrich Borgmann, mother Maria Elisabeth Sonnekers. (M.Schreiner research)