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You must have permissions to send as the mailbox first.
For the new outlook:
Click New Mail
Click open in new window
Click Options and then check Show From
Click the drop down arrow next to your email address and select the correct account
For the old Outlook:
Click New Email
Click Options and then the three dots, then click From under Show Fields
Click the From drop down
You may need to click Other Email Address and type the address into the pop-up box the first time. After that it will show up as an option that you can click on.