The properties of energy transfer in the kinetic range of plasma turbulence have fundamental implications on the turbulent heating of space and astrophysical plasmas. It was recently suggested that magnetic reconnection may be responsible for driving the sub-ion scale cascade, and that this process would be characterized by a direct energy transfer towards even smaller scales (until dissipation), and a simultaneous inverse transfer of energy towards larger scales, until the ion break. Here we employ the space-filter technique on high-resolution 2D3V hybrid-Vlasov simulations of continuously driven turbulence providing for the first time quantitative evidence that magnetic reconnection is indeed able to trigger a dual energy transfer originating at sub-ion scales.