Is the return of the first wife considered valid before the expiry of her iddah and without a new contract, knowing that the husband told her, "You have returned to me," and her family witnessed that?

The return (rujoo') is valid by the consensus of jurists through an explicit statement, such as saying "I take you back" or "I take her back." However, they differed on its validity through an action, such as intercourse or its preliminaries. It is not a condition for the return that it be done through an authorized person or with witnesses, but witnessing is recommended based on the Almighty's saying: (And call to witness two just persons from among you). Nor is it a condition for the woman to return to her husband's house. If a man says to his wife during her 'iddah (definition): "You have returned to me," this is a valid return, and she is his wife, unless the divorce was through khul' or an irrevocable divorce in exchange for compensation, in which case she does not return except with a new contract and dowry.