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This talk is based on a joint work by A.Alekseev,N.Kawazumi,Y.Kuno and F.Naef,and is a sequel to the talk by Nariya Kawazumi.In Part Ⅱ,after a brief review of the content of Part Ⅰ,we would like to explain how any solution of the Kashiwara-Vergne problem gives rise to a formal description of the Turaev cobracket for a surface of genus 0.