See that header in your Facebook notification email that looks like this?

    X-Facebook: from zuckmail ([NzYuMTY5LjIzLjU2])

That's your friend's IP address:

    % perl -MMIME::Base64 -le 'print decode_base64("NzYuMTY5LjIzLjU2")'
    76.169.23.56

[Slow-clap animation goes here.]