Send As permission on Office 365 not with Add-ADPermission
With an On-Premises Exchange 2010 environment an administrator hands out Send-As permission with the Add-ADPermission cmdlet. But I found out that this doesn’t work in Office 365. In this case a P plan (no Dirsync, Federation or such), you can see the result in the screenshot: Funny thing is that if you try Add-MailboxPermission to add Send-As permission, the error message redirect you to Add-ADPermission. For handing out Send-As permissions (and other rights) in Office 365, you’ll have to use
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