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You are only liable back to when you first started operating the business - nothing before then regardless if someone else was operating the same business in the same location.
Did you file for licensing when you first opened?
They can ask and obviuosly you don't have any information prior to when you started your business and therefore can't supply them with information as they requested.
You just have to inform them of when your business started, show them the lease, the corporation filings, and your records. You are only liable back to when you started your business.
The fact that the prior business may have operated illegally is not your concern nor problem.