Envelope: Addressed to Serials Librarian (serials = a title published on some kind of schedule, such as one every year). Sure, fine. We don't have one, per se, but it's a reasonable job title. At our library I get this kind of mail because I am the filter to decide what actual librarian to distribute it to (based on subject area).
Letter inside: Addressed to Serial Librarian. This sounds like something else entirely...
Letter inside: Addressed to Serial Librarian. This sounds like something else entirely...