I've saved the profile on a flash drive by using the Import/Export feature of the Windows Thunderbird. However, the Thunderbird in Ubuntu seems to be a reduced version of the Windows one.
In the Import wizard under the prompt: "please select the type of file to import" it is not possible to enter anything, so I cannot direct the wizard to the saved profile (exported from the laptop).
Also, I don't want to do a profile replacement, as I've got some emails in the Thunderbird on Ubuntu and wouldn't like them to be overwritten. Please note the desktop Thunderbird is set to IMAP, whereas the laptop Thunderbird contains old emails and is not connected to the server.