3569458 - Send Quality notifications and tasks via Outlook email - S/4Hana Public Cloud

You wish to send notifications of quality tasks assigned to users via Outlook email, instead of only through "My Inbox" app. 

SAP S/4Hana Cloud Public Edition

The quality notification can be send via email because of the printing function for it. However, there is no printing function for quality tasks, so you cannot email a task just like a notification. See: Printing or Sending Quality Notifications.

There might be a solution for your requirement, that is using the follow-up action for a task. However, since it is a consulting topic, this must be checked local development or consulting team. See: Defining Follow-Up Actions for Notification Tasks.

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SAP S/4HANA Cloud Public Edition 2408 ; SAP S/4HANA Cloud Public Edition 2502