im having trouble understanding this but ill tell you a few things that will make this easier for you to solve
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if the game is on cartridge, the save is on the cartridge too, so your save file on that game can be played on any 3ds without a system transfer
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to transfer the save of a digital game (not modded) you would have to do an entire systen transfer
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simply moving the contents from the sd card from your old 3ds sd card to your new 3ds sd card will not work, as all data is encrypted to the spsecific console, a system transfer un encrypts it and transfers it to the new system
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if you mod your device (if its not modded already) it is extremely easy to copy saves back and forth and would not require a system transfer
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since it seems like your old console is modded you wont be able to transfer the save if it was on the sd card ad the data is encrypted to that console and can only be un encrytped via homebrewing or system transfer, hope this helps