Overview
Outlook provides the ability to send from email addresses other than your own, pending that you were granted permission by a systems administrator. The brief instructions below, detail the necessary steps to do this using the web version of Outlook Mail.
Instructions
Step 1.
After launching Outlook on the web (https://outlook.office.com), click on the blue "New message" button in the upper-left corner of the window. When the message window opens, click on the elipsis (...) at the end of the top menu and select "Show From".

Step 2.
Click on "From" and select "Other email address...".

Step 3.
Type in the desired email address that you want to send from (You may be able to select it from the list after you start typing.).

If you have the necessary permissions to send from this address, you can proceed with completing the "To" Field, subject, and body as if you were composing/sending an email from your own address.