You are applying the force to B? Then, since the force is greater than the static friction between B and the floor, B will start to move. Once it has started to move, the problem reverts to "kinetic friction". The net force on B will be the total force minus the kinetic friction force. If that is larger than the static friction between A and B, then A will slip backwards. Static friction is not, in general the same as kinetic friction so just knowing that the force is greater than the sum of the two static frictions is not enough. It is true that, for most materials, the kinetic friction is less than the static friction. In that case, if force> static friction + static friction> kinetic friction + static friction, yes, A will move.
