(a) A municipality that creates an authority under this subchapter may annex all or part of the territory located in the authority under Chapter 43.
(b) Annexation of territory located in the authority does not affect the operation of the authority.
(c) Creation of an authority does not:
(1) affect the power of the municipality to designate all or part of an area in the authority as an industrial authority;
(2) limit a power of the municipality conferred by Chapter 42; or
(3) impose a duty on or affect the power of the municipality to provide municipal services to any area in the municipality or its extraterritorial jurisdiction that is in the authority.