Whenever a part of a municipality has been annexed to an adjoining township, which is wholly within the limits of another municipality, under the Township Code, the annexed territory may be annexed to the municipality within which the township lies as follows: A petition may be presented to the county board of the county within which is situated the annexing municipality. It shall be signed by a majority of the electors of the territory annexed to the township. If the county board finds that the petition is signed by a majority of the electors of the territory, it shall annex the territory to the designated municipality by resolution. Thereupon, except as is otherwise provided in Section 7-1-1, the limits and the authority of the annexing municipality shall be extended to include the territory previously annexed to the township.