Facebook rolled out an upgraded messaging platform in February 2011. Prior to that time, the social networking site had been offering users access to the new platform by invitation only. The upgraded service allows any Facebook user to get an @facebook.com email address. If you have an anonymous email account on another service such as Gmail, Hotmail or Yahoo! Mail, you can send a message to a Facebook user's inbox even if you aren't friends and you are not a Facebook member.
Navigate to the profile of the Facebook user that you want to message. Position your mouse in your browser's "Address Bar" and click behind the "facebook.com/" URL. Highlight the text after this URL, which is the Facebook user’s display name.
Log in to your anonymous email account on Gmail, Yahoo! Mail or any other service unrelated to Facebook. Begin a new email message. Click inside the "To:" field. Right-click and select "Paste," then type "@facebook.com" after the Facebook user’s display name.
Enter a subject for your message. Compose your message, attach any files you wish to send and click "Send" to send an anonymous email to the Facebook user.