An achievability scheme is proposed for the multiple access diamond channel with two destinations, where each base station has cached a part of the messages intended for the destination nodes. This achievability scheme is the generalization of the scheme of sending correlated codewords with the superposition structure proposed for the 2-destination multiple access diamond channel. It is shown that the achievable rate region of the scheme we proposed is the same as the achievable region of the scheme of sending correlated codewords with the superposition structure proposed for the 2-destination multiple access diamond channel without caching, but with increased backhaul link capacities by the amount of the rate of the cached information. This shows the optimality of our scheme in terms of utilizing the cached message.