When encountering an issue after changing permissions, wait for a short while for the changes to take effect, then proceed or try again:
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There is a latency involved for Microsoft Exchange configuration changes, and usually it takes a short while until freshly granted access rights become active on Exchange side.
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Missing rights (PowerShell or EWS/MAPI rights) can cause an inconsistent system state for affected mailboxes:
A mailbox synchronization process restores a consistent state, when the required rights are active during the synchronization process.
To keep a consistent state, run the mailbox synchronization process from time to time (also for purely provisioning-based systems).