"[Our ancestor]Jans Peter Aulstroupt was born in Copenhagen, Denmark ...he was a solider ... was shipwrecked in St. Croix, the Virgin Islands, and married Sara Jackson there. Among his children was Wilheim Aulstroupt, who later left and went to Puerto Rico. There he married and had children, including Peter Aulstroupt(Armstrong). Because the people had trouble pronouncing his name, Wilheim Aulstroupt was called William Armstrong. Thus, we are now Armstrong."
No one named Aulstroupt was found in the census.
A reply to this post includes the following census data for Jens Peter AASTRUP:
1855 St. Croix Census (in Frederiksted) Jens Peter Aastrup, 26, Danish, overseer
1860 St. Croix Census Little La Grange, Vestende kvarter (West End Quarter), property owned by Adam Logan Esq. Jens Peter Aastrup31 unmarried, household 31 -- also at Little La Grange, in household 3: Betsey Petersen66, unmarried Johannes Francis21 Sarah Jackson25 unmarried, Betsy's daughter <-------- William Frederik Aastrup6, Sarah's son <------ Mary Elizabeth Jackson24 Jackson Andrew3 Isaac Battiste2 Margreth7 Margreth22
Above shows that Jens Peter Aastrup is likely the partner of Sarah Jackson and father to William Aastrup - which fits the story that was told pretty well.
1840 census in Copenhagen, Denmark København, København (Staden), Sankt Annæ Vester Kvarter, Borgergade, Huuset nr. 176, 2. Sal, 173 F5, FT-1840, C5130 Søren Andersen Jeberg32 married Arbeidsmand (farmer) Maren Jeberg født Pedersdatter38 his wife Jens Peter Aastrup10 single, their son (probably stepson)