I've searched the Device sub-forum regarding this and came up with an old thread,
https://www.mobileread.com/forums/sho...d.php?t=190191 which says that cable connection is not supported so try Calibre Companion or Dropbox. Another thread suggests e-mailing.
Is cable connection still not supported? (I don't have a Dropbox account and am not familiar with CC and since this will be a once-only process due to the demise of my Sony ePub reader I'm looking for a really simple method.)
I tried e-mailing but got an automated reply saying that the my book was in an invalid format: it was already asw3 but the Amazon email-to-device process seems to expect only non-Kindle formats.
Getting my Amazon purchases into the Kindle/Nexus library is easy since they show up on the Amazon cloud. It's just my ePub to Kindle conversions that I now need to transfer.