In adsorption heat pumps, the adsorbent is typically combined with heat conducting structures in order to ensure high power output. A new approach for the direct integration of zeolite granules into a copper structure made of short copper fibers is presented here. Zeolite NaY granules with two different grain sizes are coated with copper fibers and powder and sintered to larger structures. The sorption dynamics of these structures were measured and evaluated in terms of heat and mass transfer resistances and compared to the loose grain configuration of the same material. We found that the thermal conductivity of such a composite structure is approximately 10 times higher than the thermal conductivity of an adsorbent bed with NaY granules. Sorption equilibrium measurements with a volumetric method indicate that the maximum uptake is not altered by the manufacturing process. Furthermore, the impact of the adsorbent–metal structure on the total thermal mass of an adsorption heat exchanger is evaluated. The price of the superior thermal conductivity is a 40% higher thermal mass of the adsorption heat exchanger compared to the loose grain configuration.