In the disks of four jellyfish galaxies from the GASP sample at redshift $sim 0.05$ we detect molecular gas masses systematically higher than in field galaxies. These galaxies are being stripped of their gas by ram pressure from the intra cluster medium and are, in general, forming stars at high rate with respect to non-stripped galaxies of similar stellar masses. We find that, unless giant molecular clouds in the disk are unbound by ram pressure leading to exceptionally high CO--to--$rm H_2$ conversion factors, these galaxies have a molecular gas content 4-5 times higher than normal galaxies of similar masses, and molecular gas depletion times ranging from $sim$1 to 9 Gyr, corresponding to generally very low star formation efficiencies. The molecular gas mass within the disk is a factor between 4 and $sim$100 times higher than the neutral gas mass, as opposed to the disks of normal spirals that contain similar amounts of molecular and neutral gas. Intriguingly, the molecular plus neutral total amount of gas is similar to that in normal spiral galaxies of similar stellar mass. These results strongly suggest that ram pressure in disks of galaxies during the jellyfish phase leads to a very efficient conversion of HI into $rm H_2$.