Hi @IT administrator,
Is this affected group a Microsoft 365 group or a distribution group?
Please connect to Exchange Online Powershell and run the following cmdlet to see if it works for you:
Add-RecipientPermission "Group Name here" -AccessRights SendAs -Trustee "user name here"
If the cmdlet does not work for you either, please post the error message if there is any.
If this group is a distribution group, please also try recreating it and see if it can help with this issue.
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