A little more info is needed regarding a case in Court to fully answer the question. Most likely, though, if you served the full term of suspension (which I will assume you did), DMV will usually issue a license without having to enroll in the alcohol program. HOWEVER, if you were convicted in Court for the DUI, you were likely given the alcohol program as a term of probation. If you were, and you have not completed it, then that could be the reason why DMV won't issue. But if that is the case, you may also have a potential probation violation on your hands.
I recommend you contact a local attorney and speak with them in person. Have them look up the case, if possible, to see what your probation terms were and whether a Probation Violation has been filed by the District Attorney's office.
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I am not so sure that the DMV will simply reissue after suspension. I am looking at a suspension form now which indicates that at the end of the suspension period the applicant must show proof of completion of alcohol class (among other things). This was a DMV case only; there was no court filing.
It is my understanding that the DMV requires the completion of the program not simply the passage of time for the suspension. Regularly the courts will indicate that a defendant must comply with the DMV requirements as a part of the probationary period. Failing to comply with the program may prevent you from obtaining a license.
The DMV requires the following:
1. Make it through the mandatory suspension period, complete a possible prison term, or both.
2. Complete a DUI treatment program, and then file a Notice of Completion Certificate (DL 101).
3. Make an appointment to visit the DMV to pay your reissue fee and file proof of financial responsibility (California Insurance Proof Certificate, SR 22).
4. Pay the court any fines you might owe.
If you meet certain reinstatement requirements you might be able to obtain a restricted license before you complete your mandatory suspension period.
Beyond this, you will need to speak to a DUI attorney who knows how to navigate these waters.