All taxes and special assessments which a village or city of the second class annexed under section 16-122 was authorized to levy or assess and which are not levied or assessed at the time of such annexation for any kind of public improvements made or in process of construction or contracted for, may be levied or assessed by the city of the first class. Such city of the first class shall have power to reassess or relevy all special assessments or taxes levied or assessed by any such village or city of the second class so annexed where such village or city of the second class is authorized to make reassessments or relevies of such taxes and assessments.