No, Legal Heat is a training organization that provides the requisite training course, we do not issue permits. Only the government can issue permits. At the conclusion of the course you will be provided with all the materials and/or information needed to obtain your permit. This includes a certificate of completion showing you have completed the course.
In most states permits are applied for at the local level (Sheriff or courthouse), but in some states you can simply mail in your application to the state and your permit will be mailed back to you. Depending on your jurisdiction, this process can be as quick as a few days or as long as 90 days. Your instructor will provide you with all the information regarding the application process at your course.