Although light-induced magnetostructural switching in copper(II)-nitroxide molecular magnets Cu(hfac)2L(R) has been known for several years, structural characterization of metastable photoinduced states has not yet been accomplished due to significant technical demands. In this work we apply, for the first time, variable-temperature FTIR spectroscopy with photoexcitation to investigate the structural specifics of light-induced states in the Cu(hfac)2L(R) family represented by (i) Cu(hfac)2L(Me) comprising two-spin copper(II)-nitroxide clusters, and (ii) Cu(hfac)2L(Pr) comprising three-spin nitroxide-copper(II)-nitroxide clusters. The light-induced state of Cu(hfac)2L(Me) manifests the same set of vibrational bands as the corresponding thermally-induced state, implying their similar structures. For the second compound Cu(hfac)2L(Pr), the coordination environment of copper(II) is similar in light- and thermally-induced states, but distinct differences are found for packing of the peripheral n-propyl substituent of nitroxide. Thus, generally the structures of the corresponding thermally- and light-induced states in molecular magnets Cu(hfac)2L(R) might differ, and FTIR spectroscopy provides a useful approach for revealing and elucidating such differences.