Marshpup, my apologies for the troubles you're experiencing with your Droid Turbo! Have you been able to successfully link your Facebook contacts to this phone or other phones previously? Thanks in advance for the info! Have you tried to delete your Facebook application and re-add it back to the phone? Typically the syncing contacts option is in the beginning of the app setup. I look forward to help you get this resolved!
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I have deleted FB and re-installed. I tried to link the people too. It worked just fine on both my Lumia's. I was even able to keep in contact with them, as their little faces were on my home screen and directly linked to their FB pages. Perhaps it was ONLY a Windows thing, I don't know. Trust me I am very disappointed with the Turbo and as soon as I can I will be trading it in for another GOOD phone. I tried everything anyone has suggested.
I understand your concerns regarding how your current phone sync differently to Facebook than your previous phones marshpup! A way to confirm that your contacts are in fact synced is to access your contacts on your phone and see if your Facebook contacts are also listed there. Having the little faces on your home screen may not be a feature that all phones have.
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I had a similar issue with FB on a Nexus. Nexus and Moto use Vanilla Android. At the time FB didnt play well with Google because Google was rolling out Google Plus social networking services. I used HaxSync for Facebook - Android Apps on Google Play and it properly linked the contacts within the phone.