How to Message a Nonfriend on Facebook
Sending messages to someone who is not a friend (someone who is not on your Facebook Friends list) works similarly to sending messages to friends. Because the person isn’t on your Friends list, when you type her name in the New Message screen, it won’t show up. To send her a message, you have to start by visiting her timeline.
To get to her timeline, type her name in the search text box at the top of your home page. Relevant results appear as you type. Click her name to go to her timeline. On her timeline, click the Message button in the lower-right corner of her cover photo. The New Message dialog box appears; type your message as you normally would.
Users have the option to disallow messages from people who are not their friends (or at least friends of friends). If a user chooses that level of privacy, you won’t be able to send him or her a message.
When people receive messages from a person they don’t know, they may be naturally suspicious. To avoid that, make sure you provide context in the content of your message. You’re more likely to receive a response if you explain how you know each other (mutual friends, for example) and why you’re contacting the person. In other words, include a message such as “We met at the Indianapolis Volleyball Competition.”
Links from strangers are suspicious. If you must share a link, it’s best if the link includes a preview of the destination site. Keep in mind that people are less likely to click a link shared by a stranger because of the threats of spam and phishing sites.