[grep] How to grep with a list of words

You need to use the option -f:

$ grep -f A B

The option -F does a fixed string search where as -f is for specifying a file of patterns. You may want both if the file only contains fixed strings and not regexps.

$ grep -Ff A B

You may also want the -w option for matching whole words only:

$ grep -wFf A B

Read man grep for a description of all the possible arguments and what they do.