USCIS unfortunately will not accept a simple explanation. If the documentation is incomplete (i.e. there is no proof of your having completed sentencing), then they will deny the application. This is true even if you were never sentenced, because they have no evidence to the contrary.
You need to retain a criminal defense attorney to straighten out the issue with the criminal court. If that can be done quickly, then you can likely get the response to USCIS in time. If not, you might try explaining that there was an error in the criminal records that is being rectified (or have your lawyer prepare a letter) and that you will send on the corrected information once it is obtained. They may allow you additional time then to supplement the record, instead of outright denying your I-90 application.
Good luck!
William J. Banks, Esq.
Attorney at Law
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