How to Send an Email as a Different User in Outlook

Some users have permission to send from another mailbox for special use cases. The following images are from Outlook on the desktop, but are the same for Outlook on the web.

Steps

Compose your email
Select from the top ribbon "Options" then "From"
You will now have a from drop down at the top of the message where you can select which email to send as
The first time you use it, your selection may not be present. If so then select "Other email address ..." and type in the email you want to send from

If you type in an email you do not have permission to send from, when you try to send it will fail.