As a preliminary note, if you are out of state then this is worth a try but if you are around L.A., I'm not so sure the court will accept your correspondence. So you should mention that you are out of the area now and then simply describe your circumstances, briefly, so the court can determine your request quickly and certainly provide as much documentation as possible.
I'm not saying this will work, because I don't get a lot of feedback from people corresponding, but I think at the traffic court level, its at least possible. Keep in mind, however, the courts are absolutely filled to capacity, everyday with tons of new cases on the docket and getting anything addressed by the judge can take literally months. If it's possible to hire a local attorney to go there for you, you would have a much more expedient and hands-on and managed resolution of this issue.
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In general, this requires a court apperance for a "re-referral" to traffic school. Most judicial officers will allow you to turn in the certificate if you missed the original date for turn in, as long as you aren't TOO late and you have a decent excuse. In your case, you have missed the deadline by quite a bit, but you did mail in the certificate. I would recommend contacting the court traffic clerk's office to see if you can take care of this yourself. You may need to "put yourself on the arraignment calendar" to speak with the judge. I have no idea what county you are in, otherwise I could supply you with a phone number. If they are unhelpful, you may want to contact a traffic ticket attorney.