Hello @J_sma
I would like to share following details about your ask.
If the group is being sync'd from On-Prem to Office/Azure AD then Distribution group owners must manage the group by using on-premises tools for Exchange Server such as the following:
- Exchange Admin Center
- Exchange Management Console
- Exchange Management Shell
For more details you can refer following article: Owners of an on-premises distribution group synced to O365 can't manage the distribution group in Exchange Online
If you would like to add Owners on this group, then you can use following command on your Exchange On-Prem PowerShell:
Set-DistributionGroup -Identity "Group Identity" -ManagedBy "User1"
For more information on this command, you can refer following document: Set-DistributionGroup (ExchangePowerShell).
I hope this helps and resolves your concern.
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