If that is the only conviction then the alien will likely be granted their adjustment of status. I'd encourage representation for the entire process. Our office routinely represents couples in their adjustment cases and this type of issue is fairly common for us.
Whether or not this person is eligible depends on many factors, not just a criminal record. It sounds like this offense would not disqualify someone from adjusting status, but I would definitely recommend consulting with an experienced immigration attorney.
www.gassonlaw.com - Disclaimer: This a general answer to your legal question. Unless you have a signed engagement letter with me, you should not consider this information to be legal advice.
Whenever there is a court conviction involved, you really should consult with an experienced immigration attorney, who would need to carefully review all of your documents related to the court conviction, and would then advise you on whether it would be a good idea to file for adjustment of status.
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It may be possible you should bring a copy of the arrest report and conviction record i when you consult with an immigration attorney.