Final Mem (mem sofit) is the word-final, fully closed form of the mother letter Mem, as against the open medial mem. This pair of open and closed forms drew unusual mystical attention: the Talmud (Shabbat 104a) treats the two shapes as divinely given, and famously the word 'lemarbeh' in Isaiah 9:6 contains a closed final mem in the middle of a word, an anomaly on which Kabbalists and the Zohar built teachings about hidden and revealed redemption. In standard gematria Final Mem equals Mem (40); in mispar gadol it takes the value 600. It inherits the mother letter Mem's element (Water) rather than a separate correspondence.
The five final forms are a detail the Sefer Yetzirah itself is silent on: the text as it survives knows twenty-two letters, three mothers, seven doubles and twelve simples, and says nothing about separate word-final shapes, so Final Mem's classification is inherited wholesale from Mem rather than being the text's own assignment. That base text is itself hard to date: Gershom Scholem placed its composition somewhere between the second and sixth century CE, and it survives in three recensions that disagree with each other in detail.
The Hebrew script carrying these letterforms is not the script of the earliest Hebrew inscriptions either; it develops the Aramaic chancery hand of the Achaemenid Persian empire, adopted after the Babylonian exile and standard by the Hasmonean period, displacing the older palaeo-Hebrew script, which survives afterward mainly on coins. The letter names are Northwest Semitic words inherited from that older script; their familiar pictographic glosses are modern reconstructions, and the names travelled into Greek unchanged in sound but empty of meaning.