Deuterium fractionation, i.e. the enhancement of deuterated species with respect to the non-deuterated ones, is considered to be a reliable chemical clock of star-forming regions. This process is strongly affected by the ortho-to-para (o-p) H_2 ratio. In this letter we explore the effect of the o-p H_2 conversion on grains on the deuteration timescale in fully depleted dense cores, including the most relevant uncertainties that affect this complex process. We show that (i) the o-p H_2

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... on grains is not strongly influenced by the uncertainties on the conversion time and the sticking coefficient and (ii) that the process is controlled by the temperature and the residence time of ortho-H_2 on the surface, i.e. by the binding energy. We find that for binding energies in between 330-550 K, depending on the temperature, the o-p H_2 conversion on grains can shorten the deuterium fractionation timescale by orders of magnitude, opening a new route to explain the large observed deuteration fraction D_frac in dense molecular cloud cores. Our results suggest that the star formation timescale, when estimated through the timescale to reach the observed deuteration fractions, might be shorter than previously proposed. However, more accurate measurements of the binding energy are needed to better assess the overall role of this process.