Is it valid for a husband to take back his wife after the second divorce, which was pronounced as a triple divorce, and what is the status of a third divorce after this reconciliation?

It is not permissible to issue religious rulings without knowledge. The one who ruled that the revocable return (raj'ah) after the second divorce is invalid and that the third divorce did not occur has erred. A revocable divorce is one in which the husband has the right to take his wife back without a new contract or mahr (dowry). This applies to the first and second divorces, before the 'iddah (definition) (waiting period) ends. If the 'iddah from the first or second divorce ends, the woman becomes irrevocably separated with a minor separation (bainunah sughra), and she can only return to him with a new contract and mahr. However, if the husband pronounces the third divorce, she is not lawful for him until she marries another man willingly (nikah (definition) raghbah), and then he divorces her or dies after consummating the marriage with her. This is called a major separation (bainunah kubra). The revocable return that occurred after the first and second divorces is valid. The third divorce has made your wife unlawful for you, and she has become separated from you with a major separation. She will not become lawful for you again until she marries another man willingly, and he divorces her or dies after consummating the marriage with her. A marriage of tahlil (where a man marries a divorced woman with the intention of divorcing her to make her lawful for her previous husband) is invalid.