Hello again, Michelle.
A fair resolution would depend on all of the circumstances. The employer could contact the customer, retract their statement and apologize, indicating that the employee is not a "drunk" and has been a loyal worker.
That may be enough to put this matter to rest, as it would not typically be worth pursuing compensation for the employee if the employer is willing to promptly rectify the situation, as pursuing a claim against the employer can be expensive and stressful for the employee, which they probably don't need at this point.
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