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A user who has Send As permission can't send email messages as another user account in Outlook in Office 365
Content provided by Microsoft
Applies to: Exchange Online
Consider the following two users in a Microsoft Office 365 environment, User A and User B. You use the Add-RecipientPermission Windows PowerShell cmdlet to grant Send As permission to User A for User B's mailbox. Then, you use the Get-RecipientPermission cmdlet to confirm that the permission was applied.
However, when User A enters User B's address in the From box of a new email message and tries to send that message, user A gets a nondelivery report (NDR) message that states that he or she does not have sufficient permissions. These symptoms don't occur in Microsoft Outlook Web App. User A can successfully send email messages after user A enters user B's address in the From box of an email message in Outlook Web App.
This issue may occur if the address in the From box was automatically populated by using outdated, locally cached information when User A typed User B's address. This outdated information may be used if changes to the Offline Address Book were not yet propagated to Outlook.
To resolve this issue, follow these steps:
In the new email message in Outlook, click From, and then click Other Email Address.
In the Send From Other E-mail Address window, click From, change the address book to the global address list (GAL), and then select the user to whose mailbox you were granted Send As permissions. For example, select User B.
For more information about how to troubleshoot the Offline Address Book in Office 365, see the following Microsoft Knowledge Base article:
2666477 How to troubleshoot the Outlook Offline Address Book in Office 365