Hi,
How about you use alias when you run the command Add-MailboxPermission? Just like, Add-Mailboxpermission -Identity SHAREDMAILBOX:\INBOX -User THIS_IS_A_DISTRIBUTION_LIST -AccessRights 'Author'
If the distribution list is new, you should wait for some time and run the command, maybe it needs some time to replicate.
Best regards,
Serena
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