Why did God move Gentile believers to give to the Jewish believers in Jerusalem?
God moved Gentile believers to give because the Jewish believers in Jerusalem were poor and destitute, caught in the reality that the King and Kingdom did not come. Their need was a necessity, so the collection for the Jerusalem saints was ordered, with each laying by in store as God prospered.
Les teaches from I Corinthians 16 that the collection was for the saints, specifically the Jerusalem saints. He points out Paul had given the same order to the churches of Galatia: on the first day of the week each believer should lay by in store as God had prospered, so there would be no collections when Paul came. Those approved by letters would carry the gift to Jerusalem. Les explains that God was laying on the hearts of Gentile believers the necessity of the Jewish believers who were caught in the fact that the King and Kingdom did not come, leaving them poor and destitute. II Corinthians treats this collection at greater length.
Now concerning the collection for the saints, as I have given order to the churches of Galatia, even so do ye.