As long as you don't tell the story, it's not a fake gem.
Kidd didn't steal for money, but to find a specific gem. So return or discard all other jewels that are not the target he is looking for.
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The reason involves the main plot of The Magic Fight:
Hei Yu Kuaidou learned that Kuroba Touichi, the father who disappeared eight years ago, was a black Kuroha, and his father's disappearance was related to a mysterious organization. In order to uncover the cause of his father's death, Jet Kuaidou decided to inherit his father's occupation and the name of a thief, and became the second generation of Haidong Kuroha, hoping to lead to the murderer of his father.
During an operation, Jet Kuaidou came across a mysterious organization that called him "Kuroba Touichi" and learned that the mysterious organization was plotting an immortal "Pandora's Stone of Destiny" buried in a large number of jewels, which would prevent them from killing Kuroba Touichi. As a result, Kuaidou began a confrontation with the mysterious organization, in order to find Pandora earlier than the organization and crush their conspiracy.
So Kidd is engaged in the search for this "Pandora of stone of destiny". All other targets are returned or discarded.
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Although the main plots of Magic Rush and Detective Conan are not involved, the mysterious organization in Magic Rush and the black organization in Detective Conan are also different organizations.
However, in order to keep the consistency of character setting, the Haidong Black Market in Detective Conan also continued the setting in Magic Fight-stealing gems only to find "stone of destiny".
Kidd always looks at the moon after finding a gem, because this is the way to judge whether a gem is "Pandora, stone of destiny".
See 1 episode and episode 5 of Magic Fight for details.
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hope this helps