I've got several users that were doing "send as" operations from Outlook on-prem. Upon moving them to the cloud, some still can, but others suddenly cannot.
More interestingly, the "send as" list for the account they use did not match the people actually using it. There are people not in the list that were (and still could send as) while there are people in the list that can't send as!
I corrected the list with Add-ADPermission Group -ExtendedRights Send-As -user User
entered at the on-prem server. No change whatsoever. I verified it did synch to the cloud fine. I then tried adding myself as I've never sent as before. My account propagated fine, but I also cannot do "send as" on that account.
A great many of the things I've looked at online suggestion address book problems and talk about how it will work in web but not thick client. In our case it also does not work in web and the address book fixes do not help.
I've also seen some scripts that suggest that "FullAccess" rights are required rather than just Send-As, but those scripts all fail with syntax errors as apparently "FullAccess" / Trustee commands do not work on my version of Exchange/Powershell?
Send-As permission does not synchronize automatically by Azure Ad Connect between On-premises and Office 365. However, if you add the send-as permission manually in both environments, Send-As will work in most of the scenarios.
For example, you want to grant send-as permission for an On-Premises mailbox called ONPREM1 to a cloud mailbox called EXO1, First run the following command on your on-premises server- Add-ADPermission -Identity EXO1 -User ONPREM1 -AccessRights ExtendedRight -ExtendedRights "Send As" Then run the corresponding command from Exchange Online PowerShell- Add-RecipientPermission -Identity "EXO1" -Trustee ONPREM1 -AccessRights SendAs
Reference: https://social.technet.microsoft.com/Forums/lync/en-US/d4ee2b9a-c7f2-48b2-aa05-5ed26dc0c704/cross-premises-permissions-in-exchange-hybrid?forum=exchangesvradmin https://social.technet.microsoft.com/Forums/windowsserver/en-US/e349c42e-147e-40c7-be21-2808f69137c6/crosspremises-send-as-in-hybrid-it-works?forum=onlineservicesexchange