If I post on my Facebook page and then copy the same content to my website, does Google recognize it as an unoriginal content?
Facebook pages are indexed by search engines (Google for example) and the duplicate content is detected for all indexed content.
Thus yes, Google will consider the duplicate text as duplicate content.
When content is posted to your Facebook page it:
- Links back to your site with the URL of the content
- Shows just a snippet from the content
Both of those will mitigate the damage done from Google recognizing the duplicate content. With the link back to your own site, Google will be much more likely to see your site as the original authorative source of that content. Because it is just a snippet on Facebook, Google will be more likely to send visitors directly to your site where they can view the whole thing.
For more information see: What is duplicate content and how can I avoid being penalized for it on my site?