What should I do if I paid for an employee's eduction course and he quit soon after?

You cannot deduct the cost for the continuing education course from the employee's final paycheck unless your employee manual specifies that you do so routinely in such circumstances.

Your manual must also state that you have done this in such circumstances with all others in the same situation and/or unless you had a written agreement with the employee to this effect.

Consider this a lesson learned and put the proper policy into your employee manual and use a form that is signed by any employee to whom you are providing a benefit such as training, tuition reimbursement and so forth.

It is legal to recoup your losses if you do it in this manner.