  Symmetry resolved entanglement and entanglement asymmetry are two measures of
quantum correlations sensitive to symmetries of the system. Here we discuss
their non-equilibrium dynamics in the Rule 54 cellular automaton, a simple, yet
interacting, integrable model. Both quantities can be expressed in terms of the
more analytically tractable "charged moments", i.e. traces of powers of a
suitably deformed density matrix, via a replica trick. We express them in terms
of a tensor network, which we contract in space using a system of local
algebraic relations. This gives the asymptotic form for the charged moments,
valid in the regime of large but finite time that is shorter than all the
relevant subsystem sizes. In this regime the charge moments decay exponentially
with the rate given by the leading solution to a cubic equation.
