Thanks for your response. Are you stating that there is no way of me knowing if Immigration has or will grant him permanent residency? I did not sign the I-751 and am assuming he filed with a waiver once the divorce was finalized. Immigration was formally advised that there was a divorce pending and was also formally advised by me when the divorce was finalized.

When you inform immigration that your divorce is finalized, then you're not in the picture anymore. This matter is between your spouse and immigration whether they are convinced that he entered marriage in good faith, and there were issues of domestic abuses, etc. or not. He has the right to file a waiver but it does not guarantee that he will get an approval.