Even after they arrived in Washington, the author said Mrs Obama felt rather trapped in her new home.
By contrast, her welcome by the girls of Elizabeth Garrett Anderson School was loud and enthusiastic.
Kantor writes that Mrs Obama, whose mother was a secretary, identified with the girls, two thirds of whom spoke English as their second language.
Mrs Obama, who won places at Princeton University and Harvard Law School, told them: "Although the circumstances of our lives may seem very distant I want you to know that we have very much in common."
Kantor’s book is being serialised in The Times.