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This is from the Amazon Help page:

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After you create one or more collections you wish to use for organizing your Kindle’s content, you’re ready associate items on your Kindle with those collections. Here are a few handy collection features:

Collections are stored on Amazon: When you create a collection on a device, we’ll save your collection so it appears in Archived Items on other devices registered to your Amazon.com account. This allows you to transfer collections across registered Kindles.

Books are associated with collections until removed: If you add a book to a collection on your Kindle and then delete the book from your device, it remains associated with that collection in Archive Items. If you download the book again, it will automatically appear in the appropriate collection on your Home screen.

Books can appear in more than one collection: You can associate a single book or other item from your library with multiple collections if you wish.

Collections don’t change device or Archive Items content: If you delete a book from a collection or delete an entire collection from your Kindle, it does not change the actual items saved on your Kindle or in your Archive Items on Amazon. When you delete a collection from your Kindle, any downloaded items from that collection will appear the Home screen instead of in the collection.

Thanks to Amazon Kindle Review for the heads up.

 
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