From the Super Mario Wiki
Kooper's Shell is the blue carapace that Kooper must wear in order to perform his attacks. It is stolen by Fuzzies during Chapter 1 of the game Paper Mario, along with the shells of many other Koopas.
When Mario first arrives in Koopa Village, he finds that the local Koopas are in an uproar over the Fuzzies' mischief. Kooper begs Mario to reclaim his shell from the Fuzzy in his house. Mario accepts and chases the culprit into the woods behind Kooper's house.
After cornering the Fuzzy, Mario outwits it by correctly guessing which tree it is hiding in several times. The Fuzzy returns the shell and promises to "be good from now on. Maybe." Joyous over being reunited with his shell, Kooper asks to accompany Mario on his adventure. As the heroes start to return to the village, the Fuzzy goes back on its word and attacks with three others. Mario and company chase the Fuzzies out of town, never to be seen again (not even in the closing parade).
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