Dear Ramsesan,
In such cases, evidence play the important role, as you said that, he is only suspiciouse & there is nothing any evidence against him, so, taking any action against him as unlawfull & unethical, which may create the wrong example toward existing employees.
As your are in to the contract staffing so, i do understand the client expectation & force by them.so, i would advice you that, if concern staff is really not guity in this case, then you may transfer him from from one client's location to any another client. so, your client may also get satisfaction that, suspected person is no more working in their premises & you have taken some action on their request as well as, concern employee also will not feel any unjustly happen with him.
But, still you wanted to terminate him, then as you dont have any evident of such incident, so, you may take resignation letter from him & show this case as self resignation & close the same with immediate full & final settlement of his dues.
But, still i feel that, follow this way shall treated as injustice with him or if you wanted to find the exact accused then, file the police complaint, they will identify the same.
Regards,
Tushar Swar