Beginning on Feb 3. 2016, we will be releasing an update to our Pages/Graph API which will allow Page to reply to a comment on a post with a private message. We previously announced this product on our Facebook for Business blog (https://www.facebook.com/business/news/pages-messaging-updates) and we are excited to now offer this capability to all of our partners.
When a Page responds to a comment left on a post with a private message, a direct messaging session will be opened between the Page and the person who commented, and the message will include a link to the comment for reference. Also, the comment shows a note that the Page responded privately, so other Page visitors know that the request was handled. This provides businesses with another way to deliver great customer service on Facebook and the ability to respond to specific or personal questions in a private channel.
For details and other information about this change , please review