  In this paper we continue the programme initiated in Part I, that is the
study of entanglement measures in the sine-Gordon model. In both parts, we have
focussed on one specific technique, that is the well-known connection between
branch point twist field correlators and measures of entanglement in 1+1D
integrable quantum field theory. Our papers apply this technique for the first
time to a non-diagonal theory with an involved particle spectrum, the
sine-Gordon model. In this Part II we focus on a different entanglement
measure, the symmetry resolved entanglement, and develop its associated twist
field description, exploiting the underlying U(1) symmetry of the theory. In
this context, conventional branch point twist fields are no longer the fields
required, but instead we must work with one of their composite generalisations,
which can be understood as the field resulting from the fusion of a standard
branch point twist field and the sine-Gordon exponential field associated with
U(1) symmetry. The resulting composite twist field has correlators which as
usual admit a form factor expansion. In this paper we write the associated form
factor equations and solve them for various examples in the breather sector by
using the method of angular quantisation. We show that, in the attractive
regime, this is the sector which provides the leading contribution to the
symmetry resolved entropies, both Renyi and von Neumann. We compute the latter
in the limit of a large region size and show that they satisfy the property of
equipartition, that is the leading contribution to the symmetry resolved
entanglement is independent of the symmetry sector.
