  This work presents the building-blocks of an integrability-based
representation for multi-point Fishnet Feynman integrals with any number of
loops. Such representation relies on the quantum separation of variables (SoV)
of a non-compact spin-chain with symmetry $SO(1,5)$ explained in the first
paper of this series. The building-blocks of the SoV representation are
overlaps of the wave-functions of the spin-chain excitations inserted along the
edges of a triangular tile of Fishnet lattice. The zoology of overlaps is
analyzed along with various worked out instances in order to achieve compact
formulae for the generic triangular tile. The procedure of assembling the tiles
into a Fishnet integral is presented exhaustively. The present analysis
describes multi-point correlators with disk topology in the bi-scalar limit of
planar $\gamma$-deformed $\mathcal{N}=4$ SYM theory, and it verifies some
conjectural formulae for hexagonalization of Fishnets CFTs present in the
literature. The findings of this work are suitable for generalization to a
wider class of Feynman diagrams.
