What is the Shariah ruling on a husband taking back his wife with a new marriage contract and new conditions, without documenting the previous divorce, while the first contract remains valid?

If a man divorces his wife with the first or second pronouncement and her waiting period (iddah (definition)) has expired, he may take her back with a new marriage contract that fulfills all conditions and pillars, including the woman's consent, the guardian's consent, two witnesses, and the dowry. Registering the marriage or divorce in court is not a condition for its validity; rather, it is a safeguard for rights. There appears to be no impediment to contracting the marriage and relying on the previous documentation.