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They can change the charges and either make them higher or, in this type of case, lower.
This is a common mistake. The reason is that the computer systems the police officers use in their cars aren't always accurate on what is a conviction and what is an arrest. Likely it is showing one of the arrests and one of the conviction as two different charges. There are a lot of reasons that could happen all the away from a mistake in entering the data to a mistake by the officer in reading it.
You, yourself, can't argue anything, your lawyer has to do it. This will all be cleared up when the DA runs the NCIC criminal
history. It will show the actual number of convictions.
The only big issue is if there is a conviction on your record which actually belongs to someone else. This is rare but it does happen. If it turns out that is the case then your lawyer can ask the DA to order copies of the records in the incorrect case and when they get them in it will show that it is another person based on pictures, fingerprints, D/O/B, etc.
There isn't any kind of civil lawsuit possible on this, assuming that the police officer didn't do it on purpose.