We have released the private reply to Facebook comments feature.
It is now possible to respond via Messenger to a comment on your page.

A “Message” button is now available next to the comment. Clicking on the button will open a popup allowing the customer support agent to reply to the comment via Messenger.

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Once the reply is sent, an event will be displayed in the comment ticket along with links to the Messenger ticket where the reply is.

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On the Messenger ticket, the comment will also be shown above the private reply.

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Check out this demo video: https://www.loom.com/share/266c075f34994388bd97d04cdd5b6957