Background: Inelastic neutrino-nucleus scattering is important for understanding core-collapse supernovae and the detection of emitted neutrinos from such events in earth-based detectors. Direct measurement of the cross sections is difficult and has only been performed on a few nuclei. It is, therefore, important to develop indirect techniques from which the inelastic neutrino-nucleus scattering cross sections can be determined. Purpose: This paper presents a development of the (Li6,Li∗6[T=1,Tz=0,0+,3.56MeV]) reaction at 100 MeV/u as a probe for isolating the isovector spin-transfer response in the inelastic channel (ΔS=1,ΔT=1,ΔTz=0) from which the Gamow-Teller transition strengths from nuclei of relevance for inelastic neutrino-nucleus scattering cross sections can be extracted. Method: By measuring the Li6 ejectile in a magnetic spectrometer and selecting events in which the 3.56 MeV γ ray from the decay of the Li∗6[3.56MeV] state is detected, the isovector spin-transfer selectivity is obtained. High-purity germanium clover detectors served to detect the γ rays. Doppler reconstruction was used to determine the γ energy in the rest frame of Li6. From the Li6 and 3.56 MeV γ-momentum vectors the excitation energy of the residual nucleus was determined. Results: In the study of the C12(Li6,Li∗6[3.56MeV]) reaction, the isovector spin-transfer excitation-energy spectrum in the inelastic channel was successfully measured. The strong Gamow-Teller state in C12 at 15.1 MeV was observed. Comparisons with the analog C12(Li6,He6) reaction validate the method of extracting the Gamow-Teller strength. In measurements of the Mg24,Nb93(Li6,Li∗6[3.56MeV]) reactions, the 3.56 MeV γ peak could not be isolated from the strong background in the γ spectrum from the decay of the isoscalar excitations. It is argued that by using a γ-ray tracking array instead of a clover array, it is feasible to extend the mass range over which the (Li6,Li∗6) reaction can be used for extracting the isovector spin-transfer response up to mass numbers of ∼25 and perhaps higher. Conclusions: It is demonstrated that the (Li6,Li∗6[3.56MeV]) reaction probe can be used to isolate the inelastic isovector spin-transfer response in nuclei. Application to nuclei with mass numbers of about 25 or more, however, will require a more efficient γ-ray array with a better tracking capability.