Distribution Lists are called Google Groups. If you are setup to manage on you can make changes from a web browser.


Please check out this article by Google on how to access and make changes.


https://support.google.com/groups/answer/2465464?hl=en 


Follow the "Add people to your group directly" section and follow the setups for "Using new Groups".  See the below pictures for some clarification if needed.


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You should see a list in My Groups like this, click on the add button


Once that is done please add the new account to the "Group Members" section as indicated. Do not change anything else (you want Subscription to All Email and to add Directly). You can skip the welcome message if you wish, or you can put in friendly message and it will email them that they were added.