What finally convinces the villagers to accept rip van winkles story

It was Peter Vanderdonk, a descendant of a historian, who convinced the villagers to accept Rip Van Winkle's story. He said that everything Rip described about the time period he was coming from was true, and that there was no need to doubt his words. Thus, everyone believed Peter (as he was a successor of a learned man) and Rip was readmitted into his society.