You'll have to file a motion for release from supervision in the sentencing court.
Being in another state makes it more difficult but more likely to be successful in my experience. The key is to get the written recommendation of your probation officer. If your probation officer in Georgia, your employer, your family, and any other references will write the court a letter recommending that you be released from supervision and all other conditions have been met then the court will often look favorably on your request.
The only thing I see working against you here is that judges will want long periods of drug testing on narcotics convictions. This makes it all the more important that your probation officer writes you a recommendation letter.
There is not guarantee that you will be released, but filing a motion to be released from supervision in the sentencing court (New Mexico court) is how it can be done. It will be best to use a local attorney to handle the paperwork and court appearance and in my experience you would have more likelihood of success with a personal appearance on your court date. Hopefully the judge will look at you, the recommendations, and your institutional and supervision record and see fit to release you from active supervision. In your motion you should also include reasons for wanting off supervision (conflicts with work, financial burden, etc).
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