There are some rare SharePoint cases where your SharePoint can send alerts to Users but doesn’t want to send anything to Distribution Groups.
If your SharePoint sends emails to users it means that your SharePoint outgoing email is well configured. The problem actually comes from Exchange.
Go into Exchange Management Console> Recipient Configuration > Distribution Groups.
Right-click the Distribution Group that doesn’t work, and go into Properties. Than go into Mail Flow Settings, and go into the Properties of Message Delivery Restrictions.
You have to un-check the “Required that all senders are authenticated” check box.
Now your SharePoint will be able to send emails to that distribution group.
Say Thanks if it helped :).