That when any cemetery shall be vacated as provided in this act, the said trustees or common council shall cause all the dead bodies and remains buried in such cemetery to be re-interred in the cemetery of such city or village, if they have one, and if not, then in some suitable cemetery not more than 6 miles from the nearest corporate limits of said city or village in a prudent, careful and respectful manner, and shall cause to be removed and again erected over the proper remains, all permanent fences around graves and lots, all tombstones and monuments, with as little injury as the case will admit, Provided, That no removal of said bodies and remains shall be made during the months of June, July, August or September, such removal, and the costs of the proceedings under this act, shall be at the expense of and paid by the city or village in which such cemetery is located.