What is the Sharia ruling regarding a husband who swore an oath of divorce upon his wife that she should not give a certain person a sum of money, and then found out five months later that she had given him the money, bearing in mind that this is the second time this has occurred?

No conditional divorce has occurred. If the wife gives the money to the intended person, then divorce occurs. If you had divorced her before that, then two divorces are counted, and you may take her back if she is within her iddah (waiting period). If her iddah has expired, she cannot return except with a new marriage contract. If the wife gives the money, then the divorce takes effect. However, if your mother or someone else gives the money, then no divorce occurs.