Thank you for your suggestions, but I couldn’t solve the problem anyway.
I added a Facebook App ID, all my publishers allow followers and added our website to their “linked publications” as suggested by the thread. Still nothing.
It is true that last year FB stopped the authorship for a bit, but I’m positive that it is working now (I can see it in some pages that I follow).
Yet, the plugin doesn’t seem to add it to our posts.
