If he took a conviction, then he is stuck with it. There are a couple of extraordinary measures he can look into but they are both long shots and fairly expensive. You can hire an appellate attorney to review the case to see if he has grounds to file a writ of habeas corpus. The other option is a pardon from the governor. Both are unlikely but you probably have a better chance with a writ than a pardon. Call appellate attorneys in your area to discuss the facts of the case.
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I would add that if he has a conviction for a Class A assault, that immigration can treat this as a "felony" under the immigration code even though it is only a misdemeanor in the penal code. This could complicate your husbands ability to renew his papers or obtain a visa to another country. You should consult with a criminal lawyer who is also familiar with immigration issues before putting forth the effort of going to Canada if he is not going to be eligible to do so in the first place.
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