There are a few options described here:

https://support.mozilla.org/en-US/questions/1148390

Thanks :-))

Hello there, The few options described in the article technically 'work', i.e. exporting Google Contacts to a cvf or cfv file and importing the corresponding file into Thunderbird Address Book. However, quite a few contact fields are NOT imported, mainly alternative email addresses, phone numbers, etc. Also the add-on designed for sync Google contacts and Thunderbird Address book is not functional any longer. I am in the process of a total migration and so far I was able to sync mails and calendar. However, since contacts are missing or wrong, I'm afraid there is not going to be a true migration. Thanks!

If you aren't getting all the contact fields to import with the simple approach, you should export from Google to a csv file and edit the csv in a spreadsheet so the fields match the structure of the TB address book:

http://kb.mozillazine.org/Import_address_list_from_text_file

Then, when you import the csv to TB, the input fields will match the address book fields.

Thanks, makes sense... It's a lot of work and after that I presume there won't be synchronization with new contacts created, say, when using a cellphone. Am I right? Cheers and thanks again

If the gContactSync add-on isn't working, then you won't be able to sync Google contacts with that add-on, but it's possible to sync with other CardDAV and EAS services with TbSync.