How to automatically share all the emails sent using group email address (as the group From address) with all the group members?

How to automatically share all the emails sent using group email address (as the group From address) with all the group members?

I have a group with an option "Allow members of the group to send email using Group Email Address as From address" enabled. I also have steams enabled for the group.

Is it possible to automatically share all the emails sent using group email address (using From address) with all the group members? It seems such an email doesn't automatically pop up in the group streams.