  It is shown that in the case of the forward scattering the most part of the
difference between the M\"obius form of the BFKL kernel and the BK kernel in
the next-to-leading order (NLO) can be eliminated by the transformation related
to the choice of the energy scale in the representation of scattering
amplitudes. Change of the nonforward BFKL kernel under this transformation is
derived as well. The functional identity of the forward BFKL kernel in the
momentum and M\"obius representations in the leading order (LO) is exhibited
and its NLO validity in N=4 supersymmetric Yang-Mills theory is proved.
