Does a divorce take effect upon the husband's saying to his wife: "If this statement is true, then you are divorced, divorced, divorced," three times, if the husband is not certain of the statement's veracity?

Accusing a Muslim based on mere suspicion is a grave sin, as Allah Almighty says: "O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin." (Quran 49:12), and as the Prophet, peace and blessings be upon him, said: "Beware of suspicion, for suspicion is the falsest of speech."

Therefore, your accusation of your husband's sister of theft without proof is a sin for which you must repent and seek forgiveness. The fundamental principle is to think well of a Muslim. As for your husband's statement, it is a conditional divorce dependent on the truth of what he heard about you. If it is true, then the divorce has occurred. There is a difference of opinion on whether it counts as three divorces or a single one. It is advisable to refer to the Sharia courts to rule on such matters.