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?

How to activate a conversation with the visitor on fb page?

Hi everyone!

The question is simple..
I have a fb page and I want to automatically start a conversation whenever a new visitor comes to my page without the need to click the 'Message' button.

Here is an example of what I want to do:

I'm not sure if this can be done within fb or by using an external plugin. Any help would be much appreciated! :)