Thank you very much mergen3107.
Your indicated post was indeed quite insightful insofar as I had no idea that that "random" number represented the ID.
I noticed that since I'm using the same amazon account and have changed the new device name to the old device name (don't know if that makes a difference...) the ID seems to be identical and I don't even have to change it on the new device.
Just coppying the books (.azw3) and .SDR folders (.with azw3r and .azw3f extensions) works fine and annotations and highlights are shown on kindle.
Unfortunately, that didn't quite solve my problem.
My goal is to synchronise my books in the cloud on the new device (so I can edit books on all devices and won't risk loosing annotations, etc again).
For that I need to send them via email and will end up with either a .mobi or a .azw book file (depending on conversion), but so far have worked out no way of getting a .azw3 file when sending it to the device. (If that was possible, that would be the easiest solution for me!)
That is the core of my problem, since I cannot use the backed-up .SDR folders of my .azw3 books. The extensions are just different (for example for .mobi the metadate files are .mbs, .mbp1, etc) and can't be replaced by .azw3r or .azw3f metadata files.
That's why in my naivety I thought it would make sense to convert the .azw3r and .azw3f files into .mbs and .mbp1
Any suggestions?