Hi James

There isn't a direct way I can think of to email a student upon course completion.

Some suggested workarounds (in order of my preference)

• creating a program completion message  and adding the course as the sole course or course set 
• use the Certificate module with the option to email learners and trainers on receiving certificate and there is a string emailstudenttext that can be modified in language customisations to edit the contents of the email.
• setting up event monitoring  on the course completed event and subscribing to this 
  

There is a feature request for this you can add your support to

Regards