How to make customer service be forwarded by e-mail

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Hi, I am not sure if I just can not make a function work or if it is not ment to work like that.

In customer service, we are getting all kinds of questions or orders via the contact form. How can I be notified with thees messages directly to my email.
Are these messages ment to be delt with only in BO? Because it sure is a lot more convenient to at least be notified by email - best would be if this was a imap solution where the messages were synced with my email client and updated if I answear via emailclient as well. As of now, I can only make the emails go from my emailclient to BO and sertainly not sync like I expected a IMAP service to do.

What am I missing here? 

Thankful for all responses.

🐵