Aims. We aim to determine the star formation history (SFH) of the progenitor of the Helmi streams. Methods. From the 5D Gaia EDR3 data set, we extract local samples of stars dominated by the Helmi streams, and the Galactic (thick and thin) disc and halo. We do this by identifying regions in a pseudo-Cartesian velocity space (obtained by setting line-ofsight velocities to zero), where stars belonging to these components, as identified in samples with 6D phase-space information, are predominantly found. We make use of an updated absolute colour-magnitude diagram (aCMD) fitting methodology to contrast, for the first time, the SFH of a disrupted accreted system -the Helmi streams-to that of the average Milky Way inner halo. To this end, special attention is given to the correct characterisation of Gaia completeness effects and observational errors on the aCMD. Results. We find that the progenitor of the Helmi streams experienced an early star formation but which was sustained for longer (until 7-9 Gyr ago) than for the Milky Way halo (10-11 Gyr ago). As a consequence, half of its stellar mass was in place ∼ 0.7 Gyr later. The quenching of star formation in the Helmi streams progenitor, together with some hints of a star formation burst at ∼ 8 Gyr, suggest it was accreted by the Milky Way around this time, in concert with previous estimates based on the dynamics of the streams.