Hi,
If you want to receive notifications of new messages by e-mail, you can set an additional email address in Contact Form 7 which you’re using as front-end contact form. To do this, go to Forms, choose the contact form you want (if you have more than one form), edit form and go to additional headers field. You can add Cc or Bcc header to send copy of mail message. See Adding Cc, Bcc and Other Mail Headers.