Recording of dynamic holograms in the near infrared spectral range is reported for a liquid crystal light valve with a GaAs semi-insulating substrate. The interaction of weak signal and strong pump waves are studied. It is demonstrated that an out-of-phase local dynamic grating is recorded. Optimal amplitude and frequency of the applied voltage are found for maximum amplification of the weak beam. Step-like external phase modulation of the signal wave with amplitude π/2 is used to change the type of response from local to nonlocal and to achieve in such a way additional transient signal beam amplification. Study of the cells with different thicknesses of the liquid crystal layer at different grating spacings allows a seventeen-fold gain of the weak beam in the device with the thickest liquid crystal layer of 16μm at a grating period of 1000μm (the largest possible in our set-up). The amplitude of the refractive index modulation and nonlinear coupling constant n2 are estimated from the experimental results.