  The time evolution of the entanglement entropy is a key concept to understand
the structure of a non-equilibrium quantum state. In a large class of models,
such evolution can be understood in terms of a semiclassical picture of moving
quasiparticles spreading the entanglement throughout the system. However, it is
not yet known how the entanglement splits between the sectors of an internal
local symmetry of a quantum many-body system. Here, guided by the examples of
conformal field theories and free-fermion chains, we show that the
quasiparticle picture can be adapted to this goal, leading to a general
conjecture for the charged entropies whose Fourier transform gives the desired
symmetry resolved entanglement $S_n(q)$. We point out two physically relevant
effects that should be easily observed in atomic experiments: a delay time for
the onset of $S_n(q)$ which grows linearly with $|\Delta q|$ (the difference
from the charge $q$ and its mean value), and an effective equipartition when
$|\Delta q|$ is much smaller than the subsystem size.
