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For example, in the tale of the tortoise and the hare the tortoise's victory and the social acceptance it wins would be the step that proves to the reader that committing to being “slow and steady” is beneficial.
I think “climax” would work but I would like to emphasize the judgment aspect of the scene/moment.
The term you are looking for may be epimythium. When a similar lesson is given before the fable, it is called promythium. There is a difference between these two terms and the better-known term moral. Laura Gibbs's translation of Aesop's Fable (Oxford University Press, 2002) gives an example in the context of a discussion of the fable of the ant and the cricket (also know as The Ant(s) and the Grasshopper). The fable is followed by the following words (italics from the original):
This fable depicts lazy, careless people who indulge in foolish pastimes, and therefore lose out.
Gibbs then explains the difference between the epimythium and a moral:
Unlike the moral which is fully immersed inside the table (i.e., the witty and vicious words spoken by the ant), the promythium or epimythium draws an explicit link between the world of the fable and the world in which all of us lazy people live. This link between the fable world and our own world is a key element in the fable's didactic function, and a promythium or epimythium explicitly promotes this process of identification.
See also epimythium in the Algemeen letterkundig lexicon (in Dutch).
Edit in response to the question, "How would one use this in a sentence? Would it go like “in the epimythium the author...”, “using epimythium the author implies…" or something else entirely?"
Below are a few examples from scholars discussing how authors use the epimythium.
From Ethics in Aesop's Fables: The Augustana Collection by Christos A. Zafiropoulos (Brill, 2017; page 7):
The last element of a Greek fable, although outside the narrative chain, is the epimythium (Nøjgaard calls it la moralité). (…) In the epimythium the unkown compiler [of the Augustana Collection] has singled out the point that he we wanted to draw from the fable. In this sense, the epimythium is a later addition to the fable and sometimes an abrupt one.
From The Anthropology of Wisdom Literature by Wanda Ostrowska Kaufmann and Hanna W. Kaufman (Greenwood Publishing, 1996; page 8):
In this case there seems to be a discrepancy between the moral expressed in the epimythium and the tale, which tells of a man who saves a friend falsely accused of a murder by claiming responsibility for the crime.
For fables and texts with fairly explicit messages, I would call that the moral.
I don't know if there is another, more explicit, word for the point in the story where the author emphasizes the moral. You could say the author reveals the moral by ...
