In order to send from a shared mailbox, you must have the delegate permissions to do so, otherwise you will receive an undeliverable message.
Select 'New Email'.
Next, select the 'Options' tab.
Under Show Fields, select the option for 'From'.
Now that the From field is enabled, your email address will show by default.
If you have permission to send on behalf of another user, select 'Other Email Address'.
A dialog box will appear, please type in the users address there. It will then appear as a drop-down in the From field.