Firefox bookmarks are not automatically backed up with User Data. Follow this guide to manually back them up.
Step-by-step guide
In Firefox:
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Press the "ALT" key to bring up the Firefox Menu at the top of the browser.
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Choose the "BOOKMARKS" item.
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Choose "SHOW ALL BOOKMARKS".
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A new window will pop up. At the top of the new window, click the "IMPORT AND BACKUP" button.
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In the menu, choose "BACKUP".
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A new window will pop up. Navigate to your DESKTOP folder and save the file. Keep the default name (example: "bookmarks-2015-03-05").