Every countably infinite group is almost Ornstein

We say that a countable discrete group $G$ is {\em almost Ornstein} if for every pair of standard non-two-atom probability spaces $(K,\kappa), (L,\lambda)$withthesameShannonentropy,theBernoullishifts$G \cc (K^G,\kappa^G)$and$G \cc (L^G,\lambda^G)$ are isomorphic.