As
@TheMiz suggested, I think we reuse the box the new Note was shipped in.
Here are the instructions: (It just mentions 'Shipping Box')
Step 1 - Pack your trade-in
Wrap the device with plenty of packing material such as recycled or reused paper, bubble wrap, or foam.
Step 2 - Place the device in the center of the shipping box
Cushion the device on all sides to prevent shifting that could damage the device in transit. Remove and place the lower half of the shipping label, provided via email, inside the box to ensure your order is processed correctly.
Step 3 - Seal the box
Use clear packing tape to seal all open edges on the shipping box.
Step 4 - Attach your pre-paid shipping label
Your shipping label is attached to your trade-in welcome email. Please tape all four sides of the label with clear packing tape to the outside of the box. Remember to remove or cover any old shipping labels.
Step 5 - Drop the box at a FedEx Ship Center
Please take the package to a FedEx Ship Center and hand it to a representative. Do not drop the package in a FedEx box because we will not be able to confirm your shipment.