What is the ruling of Islamic law on the deceased's sister concealing the reality of her sister's 'urfi marriage to her maternal uncle in order to ensure the wife receives her full legitimate share of the inheritance, despite this action being considered a lie?

If the deceased (husband) reviewed his wife (i.e., took her back as his wife) before the expiration of her iddah (waiting period), they do not need a new marriage contract. Otherwise, she cannot return to him except with a new contract.

The conditions upon which the validity of a marriage depends are: a guardian (wali), a dowry (sadaq), the صيغة (sigha - offer and acceptance), and two witnesses. If any of these conditions are missing, the marriage is invalid.

Intercourse in an invalid marriage, which is a matter of scholarly disagreement, and where the one engaging in it believes it to be permissible, is considered waty shubha (intercourse based on a misconception). The child born from it is attributed to the father, and inheritance is established by it if the marriage continued until the husband's death.

An invalid marriage, which is a matter of scholarly disagreement, if intercourse has occurred, entails the effects of a valid marriage. A marriage without a guardian or witnesses is a matter of scholarly disagreement.

Through such a marriage, lineage is established, and the iddah (waiting period) is due upon death, and inheritance is established if death occurs before annulment.

A woman's right to inheritance is established whether the marriage contract was valid or invalid.

Matters of inheritance are serious and complex. One should not rely solely on a fatwa; rather, they must be referred to Sharia courts for investigation and consideration of wills, debts, and other rights.