If land has been assessed pursuant to Section 18324, the city council may proceed in all respects in connection therewith as though the street lighting system were entirely within the city limits; except that the city council may enter into a contract with the legislative body of the city or county having jurisdiction over the adjoining territory either to improve all or any portion of the street lighting system, or to have all or any portion of the system improved by the legislative body of the adjoining territory. The legislative body contracting to furnish such improvement may enter into any contract or issue any purchase order authorized in this part.