Who received approval from the Jerusalem leadership to continue ministering to the Gentiles?

Les teaches from Galatians chapter 2 that Peter and Barnabas had finally gotten the okay from the leadership of Jerusalem to continue their ministry to the Gentiles, while the Jerusalem leadership would continue their ministry to the Jew. He notes there were strings attached: the Jerusalem leaders wanted Paul to remember the poor saints in Jerusalem, who had become destitute after the events of Acts 2, 3, and 4, when they sold their goods expecting the King was coming. Les then reads Galatians 2:9, where James, Peter, and John, who seemed to be pillars, perceived the grace given to Paul and gave Paul and Barnabas the right hands of fellowship, agreeing that Paul and Barnabas should go to the heathen/Gentiles and they would go to the circumcision/Jew. He connects this to Acts 15:12, where Peter came to Paul’s rescue at the Jerusalem conference, arguing that God had prepared Peter through Cornelius so he could defend Paul’s gospel; God sees the big picture. Les also mentions that offerings from Paul’s Gentile converts, as designated in Romans 15 and 1 Corinthians 16, were for the poor saints in Jerusalem.