This is serious issue and the company should take action against thosse employee who have misrepresented their qualification and also it leads to miscoduct.
At first, you can get their documents and certificates verified from the issueing authority, whether the certificate made is authenticate and issued by your office and has been signed by duly authorised officer . If they have obtained the certificate through misrepresentation, you can take action against them based on verification report .
I feel you have to tell the others the true reason as to why the concerned person was terminated. Else, it might lead to more complications and throw a bad light on your company's ethics if the other company finds out on their own that you had not revealed the truth when you were given a chance.
Anytime, you find such gross misrepresentation by any employee, you can take very strict action and in some cases, if the company so feels, can take legal action against the concerned person.