If they're all bought from Amazon their Your Content and Devices page should do the trick.
Otherwise (e.g., books you loaded onto your Kindle while it was connected to your PC) you can use Calibre to copy them from the old Kindle to your PC (by which I mean Calibre's library) and then connect the new Kindle and have Calibre send them to it. But the collections won't be preserved with the Calibre method.
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