I doubt the the part went very far on your Champion.
You can undo the two bolts that hold the tank, and it should be right there waiting for you at the bowl inlet for the tank water.
Tell your son that toilets can be cool. Last Friday Jamie and I installed a Neorest with all the bells wand whistles.My fifteen year old son just walked by and said, "You're on a toilet forum, Dad?... Ha!".
Heated seat, heated water wash, air dry, flushing powered by a pump, and get this; when you walk up to it, the lid opens for you. When you're done, it flushes on it's own. It's all very high tech and comfortable.
A toilet like that is around $4,000
A deluxe, do it all toilet by TOTO