Once he refused to waive extradition, he started a process where Mississippi will prepare a specific type of petition to seek a Court order to force him to return to Miss. Several considerations factor into what occurs. He stops getting jail credit on the Miss. charges even though he remains in custody in La. The extradition process can take months, and during that time he is generally going to be held without bail. When he has his hearing in La. in regards to the extradition, he will be limited to addressing only several issues unrelated to the proofs the State of Miss. will use to try to convict him. He will be able to argue that he is not the person named in the extradition warrant, that he was never in the State of Miss., and that the charge Miss. wants him for is not a crime. In order to defend himself, he will have to wait until the Court orders the extradition and he is returned to Miss. (assuming that it does). If he does not have a lawyer, he needs to get legal counsel as soon as possible to make sure he understands the limitations imposed on fighting extradition. Good luck.
DISCLAIMER Since I do not practice law in your State, this answer is provided solely for informational purposes only, for you to use as a starting point when speaking directly with a lawyer in your State. This answer does not constitute legal advice, create an attorney-client relationship, or constitute attorney advertising. If he does not have a lawyer, I urge you to immediately contact an experienced criminal defense lawyer admitted to practice law in your State before you/he make any decisions about this case.