Employee Allowed To Worked Even After Submitting Fake Papers And Cheating

I recently faced a case of forgery by one of our ex employees. She was showed incorrect experience at our work place, and also made forged documents and signatures. Upon verification by the new employer, it was all exposed. Multiple points were misquoted. Wrong experience, wrong designation, wrong salary, while on probation mentioned as confirmed, etc. Even after the mismatch (which was a substantial goof up), the employee seems to be allowed to work in the organization. Is this acceptable? What can I tell the new organization? This isn't the best example because it allows multiple avenues to cheat again.
Because the forged documents can now again be used by this employee when she quits the new organization and joins some other.

I am not sure whether your passion for integrity and honesty or any other personal reasons prompt this query when the employee is no more in your service. Alternatively, the incidence also indicates how poor your management was in the matters of scrutiny of documents submitted by a new employee and his/her back ground verification. So, in my opinion, it is better to leave the matter as it is and tighten up scrutiny of documents relating to appointment and back ground verification process in future. If you get any enquiry from the person's new employer, better to limit your remarks to the period of your employment only.