Within the GASP survey, aimed at studying the effect of ram pressure stripping on star formation quenching in cluster galaxies, we analyze here ALMA observations of the jellyfish galaxy JW100. We find an unexpected large amount of molecular gas (similar to 2.5 x 10(10)), 30% of which is located in the stripped gas tail out to similar to 35 kpc from the galaxy center. The overall kinematics of the molecular gas is similar to the one shown by the ionized gas, but for clear signatures of double components along the stripping direction detected only out to 2 kpc from the disk. The line ratio r(21) has a clumpy distribution and in the tail can reach large values (>= 1), while its average value is low (0.58 with a 0.15 dispersion). All these evidence strongly suggest that the molecular gas in the tail is newly born from stripped H i gas or newly condensed from stripped diffuse molecular gas. The analysis of interferometric data at different scales reveals that a significant fraction (similar to 40%) of the molecular gas is extended over large scales (>= 8 kpc) in the disk, and this fraction becomes predominant in the tail (similar to 70%). By comparing the molecular gas surface density with the star formation rate surface density derived from the H alpha emission from MUSE data, we find that the depletion time on 1 kpc scale is particularly large (5-10 Gyr) both within the ram-pressure-disturbed region in the stellar disk and in the complexes along the tail.