You can add an email address to each contact form on your site where the submission will be sent to. This is very convenient because you are alerted immediately after a customer attempts to contact you. This is the default behavior for the plugin: a user submits a form and it is emailed to the designated addresses.
It seems that your work here is done and there is nothing else to consider in the chain of communication. Don’t forget about what may happen when something goes wrong!
What if you accidentally delete a form submission email or you have an employee that isn’t properly following up with customers? You would need to log in and see a list of all the forms that have been submitted to figure things out.
Many users are surprised to find that Contact Form 7 doesn’t save any submissions. If you haven’t handled them properly they’re gone for good. Fortunately, there’s an easy way to save every submission for your later review.