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The Send-As permission must be granted by IT before the following can be done. To submit a ticket to request permissions: General Email or Outlook Problem/Issue/Request Form
Note: These instructions are for those using the Outlook desktop client. For those using Office 365/Outlook Web Access, refer to the following for instructions: Office 365 - How to access and send email from a shared mailbox
Steps
Compose a new message from the Outlook application.
Click the Options tab, and then select the From field.
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In the message click the From box to open the dialog box. Choose Other Email Address to get the next dialog box.
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Search by using the From… button or type in the full email address in the input field.
Click OK.