I have a Kindle fire HD with a large library. bought a Kindle paper white. How do I copy my library from Kindle fire to Kindle paper white?

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Hello
To download content from the Cloud:
1.From Home, tap a Kindle content library (for example, Books) in the top navigation, and then tap the Cloud tab to view Kindle content not downloaded to your Kindle device.
2.Tap your content type to download the title to your device.
3.Tap the Device tab to view your Kindle content.

For any help visit us: Kindle Support

Yes, Kindle is a name used for all the Amazon tablets and e-readers.

Kindle 2, 4, 5, 7, 8
Kindle DX
Kindle Touch
Kindle paperwhite (1,2,3 generation)
Kindle Voyage
Kindle Oasis
Kindle FIre 7
Kindle Fire HD 6, 7, 8, 8.9, 10
Kindle Fire HDX 7, 8.9

And I probably missed some in here.

To help you delete all the books from the archived list of Kindle fire device, please follow the steps given below:
- Launch a Web browser and go to Amazon.com's Manage Your Kindle Web page.
- Click on the 'Actions' button next to the item you want to clear from your Archived Items list.
- Click on the 'Delete from library' link.
- Click the 'Yes' button to confirm your decision to delete the selected item.
- Turn on your Kindle to sync it with your digital library and clear the deleted item from the Archived Items list.

GuruAid.com

Check the Serial Number You can find this sixteen digit code in the box your Kindle came in or when you click on Settings and go to Device Info. Find your specific generation or type based on the first four characters. Kindle 2: B002, B003 Kindle DX: B004, B005, B009 Kindle 4: B00E, B023, 9023 Kindle 5: B012 Kindle Keyboard: B006, B008, B00A Kindle Paperwhite (2012): B024, B01B, B01C, B01D, B01F Kindle Paperwhite (2013): B0D4 or 90D4 Kindle Touch: B00F, B010, B011 Kindle Fire (2011): D01E Kindle Fire (2012): D026 Kindle Fire HD 7(2012): D025 and D059 Kindle Fire HD 7(2013): 00D3 and 00D2 Kindle Fire HD 8.9: B0C9, B0CA, B0CB, and B0CC Kindle Fire HDX 7: D0FB, 00FB, 00FC, 0072, 00FD, 00FE, 0073, 006C, 006D, 006E Kindle Fire HDX 8.9: 0018, 0057, 005E, 00F3, 0019, 0058, 007D, 007E, 007F - See more at: http://glyde.com/glydecast/how-to/which-kindle-do-you-have/#sthash.bAbYPdzQ.dpuf

To remove a book or magazine from your Kindle Fire HD libraries, follow these steps:

1. On the Home screen, tap Books or Newsstand to display your library.
2. Locate and press your finger on the item you want to remove. A menu appears.
3. Tap Remove from Device press the helpful button

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Music can be deleted from your Kindle Fire by pressing and holding the title from the Device tab and selecting Remove Album/Song from device. Tap Yes to confirm you'd like to delete the song or album from your device.
Music stored in Your Music Library cannot be deleted through the device. To delete music stored in your Your Music Library, visit www.amazon.com/musiclibrary.

Sign in to the kindle fire hd with your account and it should sync all your content. You may need to factory reset the fire hd if it already is setup with a different account