This is a very complicated area of the law. The answer depends on the details. So, you will need to consult with a criminal defense lawyer. But, you need a specific kind of criminal defense lawyer, one who handles what are called "writs". These lawyers generally do not limit their practice to one city or one part of the state. A few are Terry Kirk (in Austin), Connie J. Kelly (in Austin), and Randy Schaffer (in Houston). Really, the picky details are so important in these cases that the best answer that can be given here is that sometimes a writ application is successful, sometimes not, and you need to discuss it with a lawyer.
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Talk to his lawyer about newly discovered evidence if you have it.
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I agree with each of my colelagues. Start with his attorney.
In no way am I offering you legal advice, and in no way has my comment created an attorney-client relationship. You are not to rely upon my note above in any way, but insted need to sit down with counsel and share all relevant facts before receiving fully-informed legal advice. If you want to be completely sure of your rights, you must sit down with an experienced criminal defense attorney to be fully aware of your rights.