When to hyphenate "well-prepared"?

No, because you shouldn't use "well-prepared" as a verb. You might use "well prepared" as an adverb and a verb, analogous to "thoroughly prepared" in "the studying has thoroughly prepared me for the test," but as noted in a comment the idiomatic word order would be "has prepared me well."

To answer the question in the title, you should almost never hyphenate "well prepared." I would do it only to avoid ambiguity, but I can't think of a sentence containing the phrase that would be ambiguous without a hyphen.

Hyphens are useful when a noun phrase is used attributively to modify a noun, as in "green-tea wholesaler." We need the hyphen here to make it clear that we're talking about a wholesaler of green tea rather than a green wholesaler of tea.

In the case of "well prepared," however, we have an adverb modifying a past participle which will then modify a noun: a well prepared student. There's no chance someone would thing that "well" is modifying "prepared student," so there's no need for a hyphen.