False Claim Against Employer Through The State

I work as a supervisor for a security company. Recently, we had an employee who was preparing to go through a gender identity change. He asked, when hired, whether we discriminate for this. He was told no. In the approximately 2-3 months of his employment, he committed no less than 3 major offenses--any one of which were grounds for termination. We did not fire him, but continuously gave him more chances. The final offense, we were required to remove him from his posting. He was informed that as soon as a new posting became available, he would be reassigned. He waited less than one week, then resigned via email and phone call. Furthermore, we have at least one documented case in which a clients employee made derogotory comments towards him, and we immediately acted in his defense. He has now filed a discrimination claim against us with the EOEC. I am under the understanding that there is recourse for us should he sue, but my question is this: What is our recourse, if any, for a false claim with a government agency? Also, is there anything the government agency might do on their own, as a result of said false claim? Thank you.