Thank you for your reply. First, if he was an employee "at will" his employer could take an adverse employment action for any, or no, reason and with no notice or warning. Therefore, even if the complaint was unfounded, nothing in the employer's action would be considered unlawful. That assumes they didn't violate a contract that he had with them. So, he would not have any basis for an action against the employer at this time.
If the employer were to share this complaint information with a prospective employer and your husband knows that it was a false statement of fact by the person who made the statement and that the person knew it was false when they made it then, at that time he might have a defamation of character action against the employer. Again though, the information must be objectively a false statement of fact, known to be false, and shared by the employer with someone outside of their Company.
As for the person who made the statement, as I touched on above, if they made a false statement of fact that they knew was false when they made it, they made be liable for a defamation of character action. Your husband could consult with a local trial/litigation attorney about the case.
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