Thank you for your efforts and help. The crucial piece of information in my case really was the filename /var/local/cc.db only.
What worked perfectly for me, step by step, working locally with the device only, using the file manager from Vlasoftssoft's toolbox (freeware part of his otherwise shareware PBChess package):
1) On the "master device" (with reference collection configuration), copy /var/local/cc.db to /mnt/us/
2) Transfer this file to the other Kindle with
exactly the same fw version and the same library content using USB connection via an external PC. Let's say to /mnt/us/ (root of user storage).
3) On the second Kindle, rename /var/local/cc.db to /var/local/cc.db.old (just to have a backup, this step is not really necessary...).
4) On the same Kindle, copy /mnt/us/cc.db to /var/local/cc.db
5) Immediately restart this Kindle. The duplicated collections now all are there.
