Jellyfish galaxies in clusters are key tools to understand environmental processes at work in dense environments. The advent of Integral Field Spectroscopy has recently allowed to study a significant sample of stripped galaxies in the cluster environment at z$sim 0.05$, through the GAs Stripping Phenomena in galaxies with MUSE (GASP) survey. However, optical spectroscopy can only trace the ionized gas component through the H$_{alpha}$ emission that can be spatially resolved on kpc scale at this redshift. The complex interplay between the various gas phases (ionized, neutral, molecular) is however yet to be understood. We report here the detection of large amounts of molecular gas both in the tails and in the disks of 4 jellyfish galaxies from the GASP sample with stellar masses $sim 3.5times 10^{10}-3times 10^{11} M_{odot}$, showing strong stripping. The mass of molecular gas that we measure in the tails amounts to several $10^9 M_{odot}$ and the total mass of molecular gas ranges between 15 and 100 % of the galaxy stellar mass. The molecular gas content within the galaxies is compatible with the one of normal spiral galaxies, suggesting that the molecular gas in the tails has been formed in-situ. We find a clear correlation between the ionized gas emission $rm Halpha$ and the amount of molecular gas. The CO velocities measured from APEX data are not always coincident with the underlying $rm Halpha$ emitting knots, and the derived Star Formation Efficiencies appear to be very low.