To add to Brian Diggs answer.
another way using grepl will return a data frame containing all your values.
toMatch <- myfile$Letter
matches <- myfile[grepl(paste(toMatch, collapse="|"), myfile$Letter), ]
matches
Letter Firstname
1 A1 Alex
2 A6 Alex
4 A1 Bob
5 A9 Chris
6 A6 Chris
Maybe a bit cleaner... maybe?