If you require a copy of your reply notifications to be sent to a shared inbox you can configure this using the 'Forward Reply function'. This is useful for when you have a shared support or help inbox that you manage customer communications from and want to make sure none are missed.

Head to settings > Email setup

Here you can select a single email address to forward a copy of all replies to. Easy.
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If the address you want is not available in the highlighted drop down then you need to add it to the system and verify it as you have with your sending address as per the instructions here.