Ok, I have the new Facebook Messages, first thing to do, link it with Gmail, how to do it? Easy.
Go to Gmail > Settings > Accounts and Import. Then, click on “Send mail from another address”.
Click on Next Step.
Click on Send Verification.
You’ll get a verification code, copy it and then paste it in the popup window. Click on Verify.
Now, test it. This is the result. Look that the mail was send to @facebook, this is how we know that this worked.
Sadly, when you receive a “mail” to Facebook you won’t get a notification. This is very sad.