Is my oath that the contract is valid and that my sister's husband received the amount from me considered a false oath (yamin ghamus) or a vain oath (yamin laghw), knowing that he affirmed in the contract that he received the amount willingly, and that I did not pay him anything, but my mother confirmed that it was a debt owed by him to her?

The determining factor in contracts lies in their intentions and meanings, not in their words and structures. Therefore, if a contract is written in the form of a sale with a received price, contrary to the actual situation, it does not change the true nature of the contract. The outcome is that this contract is either an effective gift, if ownership and freedom of disposal have been granted, or a will, if it is contingent upon the husband's death, which is more likely here to secure the daughters. A will is valid if it is within one-third of the estate and is not for an heir. Consequently, the questioner has the right to possess what is written in the contract as a will.

As for the oath that includes the statement that the deceased received a sum of money from the questioner, this is a lie and constitutes a false oath (al-yamin al-ghamus), which is forbidden. Therefore, the questioner must repent and seek forgiveness. Most scholars believe that there is no expiation for a false oath except for repentance and seeking forgiveness, while the Shafi'is hold that, in addition to that, there is also an expiation for an oath.