  We study transfer of coherent nuclear oscillations between an excitation
energy donor and an acceptor in a simple dimeric electronic system coupled to
an unstructured thermodynamic bath and some pronounced vibrational
intramolecular mode. Our focus is on the non-linear optical response of such a
system, i.e. we study both excited state energy transfer and the compensation
of the so-called ground state bleach signal. The response function formalism
enables us to investigate a heterodimer with monomers coupled strongly to the
bath and by a weak resonance coupling to each other (F\"{o}rster rate limit).
Our work is motivated by recent observation of various vibrational signatures
in 2D coherent spectra of energy transferring systems including large
structures with a fast energy diffusion. We find that the vibrational coherence
can be transferred from donor to acceptor molecules provided the transfer rate
is sufficiently fast. The ground state bleach signal of the acceptor molecules
does not show any oscillatory signatures, and oscillations in ground state
bleaching signal of the donor prevail with the amplitude which is not
decreasing with the relaxation rate.
