If you are running Exchange 2016 and Hybrid or Exchange 2019 and Hybrid, generally managing items are done on-premise and then synced up to Office 365 with AD Connect.

I had a Shared Mailbox that was synced to Office 365 and in the Office 365 Portal, I went to Shared Mailboxes and clicked on delete and was presented with the following error:

The following error occurred during validation in agent ‘Windows LiveId Agent’: ‘Unable to perform the save operation. ‘Shared_mailbox’ is not within a valid server write scope.’

To fix this error, the Shared Mailbox has to be deleted from Active Directory on-premise and once the Sync happens to Office 365, it will automatically be removed. For anymore getting this kind of error, remember to remove the item from your local AD and not from Office 365 Directly.

Hope it helps.