  Based on the recent indications of integrability in the planar ABJ model, we
conjecture an exact expression for the interpolating function
h(\lambda_1,\lambda_2) in this theory. Our conjecture is based on the
observation that the integrability structure of the ABJM theory given by its
Quantum Spectral Curve is very rigid and does not allow for a simple consistent
modification. Under this assumption, we revised the previous comparison of
localization results and exact all loop integrability calculations done for the
ABJM theory by one of the authors and Grigory Sizov, fixing
h(\lambda_1,\lambda_2). We checked our conjecture against various weak coupling
expansions, at strong coupling and also demonstrated its invariance under the
Seiberg-like duality. This match also gives further support to the
integrability of the model. If our conjecture is correct, it extends all the
available integrability results in the ABJM model to the ABJ model.
