Apparently, you cannot paste an image into an e-mail message in Outlook Web App (OWA), because the Paste command on the Edit menu or on the shortcut menu is unavailable (appears dimmed).
This issue occurs even though you enabled this functionality, including the addition of digital signatures and encryptions in e-mail messages that are composed in OWA. (To access these settings, you navigate to Options, then to Settings, and then you click the S/MIME tab.)
A limitation in the HTML system causes the Paste functionality to appear inactive. In fact, you can still paste the image into the email message.
To paste the image into the email message, click the location where you want to paste, and then press Ctrl+V.