We study the dynamics of entanglement transfer in a system composed of two initially correlated three-level atoms, each located in a cavity interacting with its own reservoir. Instead of tracing out reservoir modes to describe the dynamics using the master equation approach, we consider explicitly the dynamics of the reservoirs. In this situation, we show that the entanglement is completely transferred from atoms to reservoirs. Although the cavities mediate this entanglement transfer, we show that under certain conditions, no entanglement is found in cavities throughout the dynamics. Considering the entanglement dynamics of interacting and noninteracting bipartite subsystems, we found time windows where the entanglement can only flow through interacting subsystems, depending on the system parameters.