OK, those are issues that you didn't explain originally.
Given your fears as to his potential actions - you would be within your legal rights to inform customers that you terminated his employ because he wasn't truthful in his application and he was a convicted criminal. That's certainly legal for your to do such.
You can also caution them about signing any contracts with him concerning your business - because he is no longer employed by your company and has no power to enter contracts on it's behalf.
I would inform the past employee that he is tortiously interferring with contractual/business relations and that any continuation of such will mandate that you seek all your available remedies including but not limited to pursuing both criminal and civil actions against him.
This page:Share: tortious interference noun
encouraging a breach, infringing on another's agreement, innerfering with contract, interfering with contractual commitments, interfering with contractual obligation, interferrng with contractual rights, intermeddling
, intermeddling with business activities, obstruction
, work against anothers contractual relationship, wrongful interference with busiiess relationships, wrongful interference with contractual relationships [http://legal-dictionary.thefreedictionary.com/tortious+interference]
Tortious interference with contract rights can occur where the tortfeasor convinces a party to breach the contract against the plaintiff, or where the tortfeasor disrupts the ability of one party to perform his obligations under the contract, thereby preventing the plaintiff from receiving the performance promised. The classic example of this tort occurs when one party induces another party to breach a contract with a third party, in circumstances where the first party has no privilege to act as it does and acts with knowledge of the existence of the contract. Such conduct is termed tortious inducement of breach of contract.
Tortious interference with business relationships occurs where the tortfeasor acts to prevent the plaintiff from successfully establishing or maintaining business relationships. This tort may occur when a first party's conduct intentionally causes a second party not to enter into a business relationship with a third party that otherwise would probably have occurred. Such conduct is termed tortious interference with prospective business relations, expectations, or advantage or with prospective economic advantage. [Wikipedia]