The fate of water which was present on early Mars remains enigmatic. We propose a simple model based on serpentinization, a hydrothermal alteration process which may produce magnetite and store water. Our model invokes serpentinization during about 500 to 800 Myr, while a dynamo is active, which may have continued after the formation of the crustal dichotomy. We show that the present magnetic field measured by MGS in the Southern hemisphere is consistent with a ~500 m thick Global Equivalent Layer of water trapped in serpentine. Serpentinization results in the release of H2. The released H atoms are lost to space through thermal escape, increasing the D/H ratio in water reservoirs exchanging with atmosphere. We show that the value of the D/H ratio in the present atmosphere (~5) is consistent with the serpentinization of a ~500 m thick water GEL. We reassess the role of non-thermal escape in removing water from the planet. By considering an updated solar wind-ionosphere interaction representation, we show that the contribution of oxygen escape to H isotopic fractionation is negligible. Our results suggest that significant amounts of water (up to a ~330-1030 m thick GEL) present at the surface during the Noachian, similar to the quantity inferred from the morphological analysis of valley networks, could be stored today in subsurface serpentine.