Mail notification for new mails in Mail App Inbox

We are using the Mail App for a shared (group) mailbox only. This means that users are managing their private mails in eg. Outlook but not in Nextcloud. These mail addresses are stored in the users profile.
We would like to get being notified by mail to the private mail address if a new mail arrives in the Inbox of the Mail App.
Does anybody know how to reach this out?