LYNN – Constituents looking for their city councilors won’t find them in the old fourth-floor office at City Hall after next week.By late November, the council will be ensconced in a new office suite farther down the hall, a sprawling space which once accommodated the Personnel Department. Contractors have already begun supervising the process of moving boxes, equipment and furniture.When the move is complete, visitors will no longer walk into cramped quarters where the desks of two administrative staffers occupy the bulk of the square footage. Also gone will be the council’s small conference room, the modest office of the council president, and a smaller room used by the other councilors for private discussions.Visitors to the new suite will be greeted by a service counter in view of Theresa Young, the council’s executive assistant, and Julia Hogan, the council aide. Councilors can stretch out with little discomfort in the spacious high-ceilinged conference room and the office of the council president, a post currently held by Councilor at Large Timothy Phelan, will rival the mayor’s office in size.”Tim designed it so that the councilors will have an area to meet their constituents,” said Young, noting that the present space for the purpose is a small room cluttered with office equipment and supplies. “Right now, it’s just a spare room. The new space will allow the councilors to talk in private to their constituents on Tuesday nights or anytime during the day on weekdays.”Once the former council offices entered through Room 408 are vacated, they will be occupied by Rosemary Sargent, a staff legislative aide to U.S. Rep. John F. Tierney, a Salem Democrat whose primary North Shore office is located in Peabody. Sargent’s office in City Hall is presently in the basement near the Personnel Department.The council’s new office address will be Room 412.”The big move will be on the 13th and from what Tim told me we’ll be up and running on the 16th,” Young said.