Based on what you are saying here, and what I am sure you told the hearing officer, you had no warnings, you had no write ups and you did not violate a company policy that was well known as instant grounds for termination. You did make this clear to them, didn't you? Though you did not have proof of this, it is sounding as if you may have been the more believable party in this hearing. You may have the decision go in your favor.
The employer did not have any documentation that showed you had been written up, warned, etc, did he? So it was just what he was saying, right? They did not have proof? How could they have, if it didn't happen? You did clearly state that it didn't happen, under oath, didn't you? So your word may be more believable than theirs.
So wait and see. Keep certifying for the weeks that pass. If it goes in your favor, that's all that needs to happen. They would have to appeal to the board of review, and they would have to submit their arguments and evidence which they apparently don't have. The board would have to determine that the law had not been followed in the prior hearing.
Even if you lose, you still cannot do anything to your employer. An employer can fire you for any reason known to man, because he felt like it if he wants to. It doesn't matter if he fired you based on lies. You cannot sue him civilly for this, as he has violated no law by terminating you and trying to keep you from drawing unemployment. You do not have a case against him for "lying in the unemployment hearing." You do not have a case against him for firing you unless it were an EEOC case, where you had been terminated because of your race, religion, national origin...any of those protected class issues. And this has not happened and would be tough to prove if it had, because they have gone with another reason, though it may have been a wrong reason.