The expiration of the term of office of any of the members or of the president of the board of trustees of the village shall automatically result in the expiration of the office of any such member of said board of local improvements, and the election of any member as president or as a member of the board of trustees shall automatically make any such person a member of the board of local improvements from the time said party duly qualifies and becomes such president or member of the board of trustees of the village. (2005 Code)