Your users can follow the steps below to send Gmail messages using a group address:

1. On your computer, open Gmail.
2. In the top right, click Settings   See all settings.
3. Click the Accounts tab.
4. In the Send mail as section, click Add another email address.
5. Add the group's email address and check the "Treat as an alias"
6. Click Next Step  Send verification.

The final step is to head back to groups.google.com and locate the verification message. Click the link to authorize your email to become an alias for the group.

Now, when you will now be able to select the Group address from a dropdown menu in your From field