Right click on the email sent to the distribution group.

From system@entrata.com, Subject 0 Seconds Lead Voicemail for The Standard, Received Wed 1:10 PM, Size 78 KB, Flag Status Unflagged, Preview Som...

Click "Always Move Messages To: " distribution group name.

Always Move Messages To: Leasing-The Standard

Select the folder you would like to move it to.

Click on the folder you selected for the rule.

You will now see the email in the folder.  All future distribution emails will come to this folder.

Setting up email rule for distribution group emails