California will not punish him for an infraction/misdemeanor in NM, but the Auto Insurance Carrier will probably pick it up on the next Credit Check at renewal. Reckless Driving will hurt; he may find himself as an Assigned Risk.
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Because of the interstate compact, California will find out about the conviction. Depending on how it transfers it can add points to your California driving record. Unless he has too many points in California, nothing will happen here.
If you have 4 points in 1 year the DMV will consider you a negligent operator and can suspend your license, 6 points in 2 years or 8 points in 3 years.
CA will definitely find out about this conviction. The CA DMV will convert points. Was this a reckless in NM? A misdemeanor? Insurance will find out too.