In this paper, we considered a molecular structure that consists of a molecular chain and an additional molecule (donor or acceptor) that can inject (or remove) single excitation (vibron, electron, etc.) onto the molecular chain. We assumed that the excitation forms a self-trapped state due to the interaction with mechanical oscillations of the chain structure elements. We analyzed the energy spectra of the excitation and showed that its state (when it migrates to the molecular chain) has the properties of the nonadiabatic polaron state. The conditions under which the excitation can migrate from one subsystem to another one were considered. It was shown that the presence of a "donor" molecule cannot significantly change the properties of the excitation located on the molecular chain. At the same time, the molecular chain can affect the position of the energy level of the excitation localized on the donor subsystem. Indirectly, this can influence the process of excitation migration from one subsystem to another one. The influence of the basic energy parameters of the system and the environment temperature on this process are discussed. The entire system was assumed to be in thermal equilibrium with the environment.