Use the Send on behalf of send permission to specify which users can send messages on behalf of the distribution group.
To modify the send permission for dynamic distribution groups
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In the Manager, select the Azure Active Directory > Tenants > <Azure Active Directory tenant> > Exchange Online administration > Recipient configuration > Dynamic distribution groups category.
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Select the dynamic distribution list in the result list.
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Select the Assign send authorizations task.
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Select the table which contains the user from the menu at the top of the form. You have the following option:
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Mail-enabled distribution groups
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Mailboxes
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Mail users
 
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In the Add assignments pane, assign users.
TIP: In the Remove assignments pane, you can remove assigned users.
To remove an assignment
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Select the user and double-click
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Save the changes.