  We study the full counting statistics (FCS) and symmetry-resolved
entanglement entropies of integer and fractional quantum Hall states. For the
filled lowest Landau level of spin-polarized electrons on an infinite cylinder,
we compute exactly the charged moments associated with a cut orthogonal to the
cylinder's axis. This yields the behavior of FCS and entropies in the limit of
large perimeters: in a suitable range of fluctuations, FCS is Gaussian and
entanglement spreads evenly among different charge sectors. Subleading
charge-dependent corrections to equipartition are also derived. We then extend
the analysis to Laughlin wavefunctions, where entanglement spectroscopy is
carried out assuming the Li-Haldane conjecture. The results confirm
equipartition up to small charge-dependent terms, and are then matched with
numerical computations based on exact matrix product states.
