Submonolayer quantum dots as active medium in opto-electronic devices promise to combine the high density of states of quantum wells with the fast recovery dynamics of self-assembled quantum dots. We investigate the gain and phase recovery dynamics of a semiconductor optical amplifier based on InAs submonolayer quantum dots in the regime of linear operation by one- and two-color heterodyne pump-probe spectroscopy. We find an as fast recovery dynamics as for quantum dot-in-a-well structures, reaching 2 ps at moderate injection currents. The effective quantum well embedding the submonolayer quantum dots acts as a fast and efficient carrier reservoir.