  We consider the form factor bootstrap approach of integrable field theories
to derive matrix elements of composite branch-point twist fields associated
with symmetry resolved entanglement entropies. The bootstrap equations are
determined in an intuitive way and their solution is presented for the massive
Ising field theory and for the genuinely interacting sinh-Gordon model, both
possessing a $\mathbb{Z}_{2}$ symmetry. The solutions are carefully
cross-checked by performing various limits and by the application of the
$\Delta$-theorem. The issue of symmetry resolution for discrete symmetries is
also discussed. We show that entanglement equipartition is generically expected
and we identify the first subleading term (in the UV cutoff) breaking it. We
also present the complete computation of the symmetry resolved von Neumann
entropy for an interval in the ground state of the paramagnetic phase of the
Ising model. In particular, we compute the universal functions entering in the
charged and symmetry resolved entanglement.
