This is possible, by using the User classes.

Login as admin and in Administration/User classes create a class (we'll call it 'Restricted') with the permission 'Send emails outside' disabled - enable other permissions as required.

Then edit the user account and assign it to the 'Restricted' class.

Important

Users can send emails either via webmail or via a normal mail client using SMTP.

Disabling the 'Send emails outside' permission always affect the webmail sending.

However to be effective on emails sent via mail clients, mail relay (in Administration/Mail/SMTP Incoming) must be disabled, and all mail clients must use SMTP authentication (see this article). This allows DeskNow to know who is trying to send the email and act according to the permissions set.