There is a risk in going ahead now with a FIR and criminal case. This being a white-collar crime, all records, documents, and other evidence have to be submitted to the police in the original, and you will be handicapped in proceeding departmentally against the employee. Secondly, the standard of proof in a criminal case is to prove the guilt beyond doubt, and also the process is a long-winding one. So you will have to keep the employee under suspension for too long.
In case you proceed with the domestic inquiry, the degree of proof is much less stringent (preponderance of probability), and the action can be relatively very quick. So you may take a call looking at all these facts. From practical experience, I can say, finish the disciplinary action fast, take action, and tie down the employee in the criminal case.
One thing remains a mystery, how an HR person could do massive swindling of finances through falsification of records; maybe others too are involved.