Hi @Giorgio Amodeo ,
Does the group you mentioned here mean the Exchange distribution group like below?
If so, as I know, the owner of distribution groups plays quite a different role with members of the group.
When creating the distribution group, the admin can choose any users in the same organization to be the owners and the members(which means the owner might not be the admin user.) and he could choose if automatically add group owners as group members and some other permissions like below:
According to my tests, if A was only added as a group owner, and after removing A from group owner, then A is no longer belong to this group. I also tried to send test email messages to this group and found that if A was only added as a group owner, he will not receive the test emails. If A is not only the group owner but also in the member list, he will successfully receive these test emails.
For more information about distribution group, please check this article: Manage distribution groups.
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