The paper studies the transfer of angular momentum across the interface of two immiscible liquids in a closed vortex flow, generated in a stationary cylindrical container by a rotating disk, being the upper endwall of the cylinder. When the disk rotates, a centrifugal force begins to act on the upper less dense liquid, which leads to the appearance of a centrifugal circulation of the upper liquid. Since the swirling flow of the upper fluid along the sidewall moves from the rotating disk to the interface, it transfers the angular momentum to the interface, thereby swirling the lower fluid as a result of the action of viscous friction. A forced circulation of the lower fluid arises. Flow visualization and measurement of the circumferential velocity component serve to determine the regularities of the formation of a vortex flow of a denser liquid located under the interface and having no direct contact with the solid disk generating the vortex motion. The development of the centrifugal circulation of the lower liquid is found to be similar to that in a mono-fluid. The obtained results are of interest for further development of vortex devices and reactors that provide complex vortex motion of ingredients for mass transfer enhancement, optimization of the operation of existing units, and for the design of new devices.