Group Email Sent Messages Not Shown To All Group Members

I am trying to understand the setup of a group incoming email address. I have two users in a Security Group sharing an address and when a new message comes in, both users can see the message just fine. However, once someone replies, only the user who replied can see the message in their “My Sent Mail” box.

Is it possible for the sent mail to just be shown in the group mail window? Is it possible for the IMAP to just show the sent mail box of from the server? I have the box designated in the Group Mail Account setup, but it doesn’t create a folder for sent mail. The user who did not reply is shown the “replied” arrow indicating someone had replied to the message. However, not being able to access that reply makes it pretty difficult to share the inbox responsibilities.