The addressbook name is abook.sqlite . If you know its location, you can import it with tools>import>import a file and proceed to addressbook and sqlite file. if the old PC is still working, you can start thunderbird on it, click help>troubleshooting information, scroll down to 'profile folder', click 'open folder' and you will be in windows file explorer (assuming you use windows) and the abook.sqlite addresssbook will be there, the addressbook for collected addresses is history.sqlite.

Thank you, I will try those things now!