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.
In the message click the From box to open the dialog box. Choose Other Email Address to get the next dialog box.
Search by using the From… button or type in the full email address in the input field.
Click OK.