How to delete conversation with someone on facebook, both from my inbox and from his inbox?

I have a conversation with someone on facebook that contains some sensible information that that person could use to harm me. What should I do to delete that conversation from both my inbox and from his inbox.

As far as I know, the delete option in facebook only works for my inbox. That means that the messages I delete, still remain in that person’s inbox.

What options do I have?