First you have to make sure the From button is displayed in your New Message Window. You can show the button by going to Options, then select From in the Show Fields group on the ribbon.
Click on the From button in a new message window.
Click on Other Email Address...
For best results, grab the email from the Global Address List. To get there, click on From
and select Global Address List. Do NOT choose OFFLINE Global Address List
Type name or scroll down to find on list.
If the display name happens to be the same, you can scroll right to view corresponding email address.
Double-click on the name to select it.
You should now see it in the From list.