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Once your new phone arrives and you've set it up, you'll receive a box and shipping label from Apple's trade-in partner to return the phone. Once it's been received and evaluated to ensure they agree it matches the condition you described, they'll inform you of the value and if there is an discrepancy.

Yes. Only send the iPhone back, not the accessories, and take photos of the trade-in iPhone from various angles and a short video of the phone working properly. Do this just before you pack it up to send.