The employer has a right to terminate the employee for any reason or for no reason at all so long as it is not discriminatory based on race, sex, age, disability or religion. Therefore, the employer can terminate the employer over something like this - even if it is not true.
However, the employee would have a right to sue the customer that made the accusations for defamation because she knowingly lied to about what happened in an attempt to harm his reputation and his employment.
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