In a previous paper [P. Hamm and J. Savolainen, J. Chem. Phys. 136, 094516 (2012)]10.1063/1.3691601, we have studied the 2D-Raman-THz response of liquid water, based on an all-atom molecular dynamics simulation. In the pulse sequence we investigated a near-infraredlaser pulse excites a vibrational coherence through a Raman process that switches it into another coherence by a THz pulse after some time, and finally read out by the emission of a THz field.In the present note, we explore the inverted time-ordered pulse sequence, in which the first coherence is generated by a direct THz excitation, while the switching of coherences is achieved by a Raman interaction. Since the dependence of the polarizibility on the nuclear coordinates is more nonlinear compared to that of the dipole moment, this pulse sequence reveals more of the couplings and correlations between the various degrees of freedom of water. Compared to 2D-Raman spectroscopy and the original pulse sequence, this pulse sequence reveals the clearest signature of a photon echo.