Google has updated the new User Interface (UI) for Google groups with two features that allow the assignment of messages and the ability to configure a default email address for sending messages from the group.
Previously, these assignments could only be made in the classic view, which will be going away soon.
Set a Default Email Address
Ensure you are using the new UI for Google groups. If you are using the classic UI, the option to go to the new UI will appear in the right-hand corner.
Visit a group where you are an owner. In the left column, select Group settings.
Once Group settings are selected, toggle the Advanced button on the top right of the page.
In the left column, select Posting policies.
Scroll down on the main page to Default sender. Click the radio button for Group address.
Click Save Changes at the bottom of the window.
Once the page is saved, refresh the page for the setting to be reflected, or close the browser tab, and open the group again.