In order to switch from one licensed producer to another, you will need to go back to your doctor and get a new medical document. Your licensed producer is not permitted to transfer your existing medical document to a different LP, nor is it allowed to mail you back your medical document. All it can do is destroy your medical document should you inform it that you’re switching to a different producer.
Once this is understood, switching producers is perhaps more straightforward, as the process is essentially the same as the one you went through to sign up with your original licensed producer. For more on how to register with a licensed producer, see this article.