You really don't have to do anything, once the new kindle is set up on your home wifi network, and registered to your existing amazon account (should have been done automatically if they replaced it under warranty, or it was purchased from your own account), then all your prior purchases will sync to the new kindle automatically.
To expedite that process, go to the kindle home page, then look for the library, and choose CLOUD library rather than device library, the first time you touch on your desired book there, it will prompt it to download immediately for use.
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