In his contract a customer refers to the J-STD-001FS. Is this a mistake in writing, since the document we use is designated J-STD-001F?

No, apparently this customer is related to the space industry. For this group of products IPC has developed a so called addendum, a document containing supplementary specific criteria. This means that this product is subject to the criteria in the regular J-STD-001F as well as J-STD-001FS (mind the priority however). Remark: J-STD-001FS should not be used in conjunction with J-STD-001E.