Arrowinmyknee
First of all, the cape that the MC put in place of the original would still work perfectly for the things harry has to do, and the other relics, the stone wouldn't interfere too much with the plot, it just depends if the dumbledore wants to die in the riddle of the prince by will or because he was already dying because of the horcrux curse, the wand if the dumbledore dies he can take his grave, the plot still won't change that much, voldemort will still use another wand to try to kill harry if Dumbledore don't die the MC has to find a way to get his wand, now... about Dumbledore finding out it's not the real cape, what can he do? the most he did is put a tracking spell on the cover, the MC has a system that analyzes even the philosopher's stone, a very complex item, seeing that it has a tracking and breaking this spell is not so difficult for the MC.
Diabolo3:Cus it would mess up the plot a lot, exept he gets a spare cloak. And even then Dumbels would 100% notice it
Sometimes I think the Author is crazy in the head, first it was the story of gold with the philosopher's stone, which won't produce much so as not to break the economy, if you don't want to break the economy, just don't use everything, stay with a little and sell it later, gold is never too much, now it's this business of taking the cape and then returning it instead of keeping it and getting the other relics.