<p>The coherent transfer of optical vortices in a four-level double-cascade cold atomic ensemble is examined, showcasing the transfer of orbital angular momentum from the incident vortex probe field to the generated signal field through the four-wave mixing process. Results indicate that, without single-photon detuning, the transfer efficiency is limited to 25% under phase matching conditions. However, in the presence of single-photon detuning, the conversion efficiency of optical vortices between the probe and signal fields can be significantly increased. Interestingly, the presence of single-photon detuning can enhance, rather than diminish, the transfer efficiency of optical vortices. Furthermore, the impact of the control field on the composite vortex formed by the incident vortex probe and signal fields was investigated. Findings suggest that adjusting the strength of the control field allows for precise control over the strength and phase patterns of the composite vortex.</p>