What is the obligation when a son acknowledges a brother, denies him, and then acknowledges a second brother, considering whether the initial payment was judicial or voluntary?

Primary text

The people of Iraq state that if the son paid the first brother based on a judicial ruling (qada'), he must give the second brother half of what remains in his possession. If the payment to the first brother was made without a judicial ruling, he must give the second brother one-third of the entire estate.