Although it hasn’t been reported on the forums, I think there was a problem with the forum’s email host or email setup in the period april-july. If your friend tried registering sometime in this period, that’s probably why he never received any confirmation email. However, this problem appears to have been fixed now.
Your friend could try one of the following things in order to activate his account:
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Request another confirmation email by using this form: https://forums.blackmesasource.com/register.php?do=requestemail
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Sign in with the account he previously registered, and change the email address in the user profile to something else. A confirmation email should be sent out to the new address. He can then later change it back to the previously used email address (which would require another confirmation).
[NOPARSE]EDITED TO ADD:[/NOPARSE] Like sersoft suggested below, check the spam folder or try using an email address from a different email provider.