How do I fetch the email of my friend programmatically in my facebook application? Does facebook provide this functionality?
The answer is no, Facebook does not provide this functionality. Facebook tries to protect the privacy of its users, and therefore user email addresses are explicitly not available.
The only way to email a user is to prompt them to grant you extended email permissions via a Facebook prompt. If they grant you the permission, you can then use the notifications.sendEmail API method, or query the user table for the proxied_email field, and send them an email via Facebook's Email Proxy system.
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proxied_email
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