Follow Up Boss doesn't sync directly with Google Contacts, but this can be done through PieSync.
This Piesync integration will allow true 2 way syncing with Google contacts.
1. Signup for a free trial here:
2. Once logged in to your Piesync account,
3. You can just follow the on screen step by step instructions:
6. Ensure that "FollowUpBoss wins" is ticked.