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We evaluate what should be the optimal simple fiscal response to a monetary shock when inequality and redistribution matter. Due to persistent high indebtedness, unemployment and increasing inequality, the evolution of the income and wealth distributions has become essential to assess the coordination of fiscal and monetary policies. To deal with these distributional issues, we study welfare-maximising fiscal response to a monetary shock using a HANK model with search and matching frictions calibrated on US data. The main results show that the most welfare improving response is through a decrease of labor income taxation. In spite of a worsening of the labor market, this leads to an overall positive macroeconomic expansion, while it provides some distributional welfare improvement for the entire wealth distribution and might trigger a trade-off between higher inequality or higher unemployment.