Many times it is possible. The issue is you need to find an equivalent course in New York. You may or may not get credit for the amount of time that you have already spent on your current DUI class. What you need to do is go back to court to get the judge to allow you to complete the remaining portion of the DUI class in New York. Make sure you do not just move, get the court order first. The other thing to keep in mind is making sure the DMV will accept the New York class as well. If the DMV does not accept the class it will create problems for you in getting a valid New York license.
In addition to the DUI program being approved by the Court in your jurisdiction, make sure you receive the DMV's approval. They are difficult sometimes to deal with when it comes to having a DUI in one state and doing a program in another. Non-compliance with their specific rules can effect getting a license to drive in New York.
You should add the case to calendar to modify the sentence. You need permission from the judge to do an equivalent program in New York. Furthermore, communicate with both the CA and NY DMV to make sure they will approve the courses. You may lose credits for the classes you've already completed.