Epymythium (plural epimythia) is a moral appended to the end of the story...but epimyth is sometimes listed with the same definition.
Greek, from ἐπί ‘upon’ + μῦθος ‘story, fable’.
'Epimyth' has been in use in English for a while; here's the definition from the 1878 book A Vocabulary of the Philosophical Sciences by William Fleming and Henry Calderwood:
Fable - The Greek writers distinguish: 1. The fable, muthon, or myth;
2. The promyth, or introduction to the fable; 3. The epimyth, coming after the fable, the moral.
So in that definition, epimyth comes at the end of the story.
But Ben Edwin Perry (Professor of Classics at the University of Illinois in the early 1900s) wrote:
"When the moral of a fable stands apart at the end, which is not always the case, we have what is properly called an 'epimythium'. Herein the author, speaking in his own person, explains to us - often against our will and Minerva's - what the preceding story means in terms of general principles. He makes an application that is always general or gnomic, never specific; and he does so usually in the spirit of an interpreter. In the manuscripts the epimythium is often called the λύσις, or 'solution', as if the foregoing fable were a riddle to be solved."
Dr. Perry went on to suggest an origin for the epimythium: he speculated that in Demetrius of Phalerum's collection of Aesop's Fables, the promythium was intended as an index-heading; later writers, believing it was explanatory, felt that the end of the fable was the more logical location, and developed the epimythium, and this became the tradition.
This is difficult to verify, since apparently there are no existing copies of Demetrius of Phalerum's collection.
The moral of this story is that you never really get to the end of the story of an English word. But it's more about the journey than the destination.