Connect to facebook page (ei. company page) through the facebook account administering that page, and also connect to you Linkedin company page through buffer.
If
New status message on page
This Trigger fires every time you create a new status message on your Facebook Page.
Then
Add to Buffer
This Action will add a post to Buffer. If your Buffer is full then the post will be skipped.
Explore more great ways to automate Facebook Pages and Buffer