Remkus/Rimkus is the name used in the US. I don't know how it was in Lithuania. 5 members (Sons&Daughters) came to the US. Louis,Peter,Joseph,Domicella & Annie.Louis was born in 1885,Joseph in 1883 and the rest are a year or so apart.
One brother is buried with the last name spelled Rimkus.
I believe they came when they were in their 20's. I know they were here at the time of the 1900 censes as they are all listed with spouses and children they had in America.
All the 5 members settled on Long Island, NY. Between Easthampton, Southampton but most in Sag HArbor, NY.In the data you asked about they are all listed as having been born in Lithuania,1 brother has Klaipeda as his home town with a wife named Caroline Brezinkis from Palanga.Having German roots as well, I was able to get information from a book that was kept in the town, does Lithuania have this type of information on it's people?