Conformal kernel for NLO BFKL equation in $\mathcal{N}$=4 SYM

Using the requirement of M"{o}bius invariance of $\mathcal{N}$=4 SYM amplitudes in the Regge limit we restore the conformal NLO BFKL kernel out of the eigenvalues known from the forward NLO BFKL result.