The cloak that does not wear out
Harry’s invisibility cloak is a family object from his father, and in the last book it is named as the cloak of the Deathly Hallows. Readers still disagree about whether that identity was fixed when the cloak first appeared.
Mise en place
1Harry Potter à l’école des sorciers · A Christmas present with no name
Harry receives a cloak that hides him completely, with a note saying it belonged to his father and that he should use it well. Dumbledore is the obvious sender. The cloak is then the way Harry breaks rules.
Other cloaks in the books fray, stick, or fade. This one does not, but the first book never says that difference is the point.
Dénouement
Harry Potter et les Reliques de la Mort · Xenophilius explains the Hallows
The third Hallow is a cloak that hides the wearer truly and does not fade with age. Harry realizes the one in his trunk is that cloak, passed from Ignotus Peverell down to James. Dumbledore later says he had borrowed it from James to study it.
The payoff on the page is clear. What stays debated is only whether the Hallow story was already the plan in the first book, or a later meaning wrapped around an object the story had used for years.
