Thank you for your response. You did correctly identify the arrival record of my great-grandfather, Morris "Mordche" Feigin. (It remains unclear to me why on the manifest he declared himself "single" and made no mention he was joining a wife in the U.S.)
"Fruma Libe" -- which is how it's usually spelled -- was a woman's name among eastern European Jews, if a quite uncommon one. If you google the name, you'll find a number of examples.
I've successfully identified the arrival records of all my relatives, except this great-grandmother. I'm attaching her certificate of arrival from her naturalization petition, for use by you and other researchers. My presumption is that she provided her arrival name -- "Froma Liba Levitt" -- to the Immigration and Naturalization Service, which was supposed to produce the certificate after checking the ship's manifest (or a microfilm copy of it) and confirming that someone with that name arrived on the given ship on the given day.
By the way, I also can't find "Froma Liba Levitt" -- or any name resembling it -- on the ship's departure manifest from Hamburg, where my great-grandmother supposedly boarded the ship.
So once again, can someone explain what's going on here?