Gas can be violently stripped from their galaxy disks in rich clusters, and be dispersed over 100kpc-scale tails or plumes. Young stars have been observed in these tails, suggesting they are formed in situ. This will contribute to the intracluster light, in addition to tidal stripping of old stars. We want to quantify the efficiency of intracluster star formation. We present CO(1--0) and CO(2--1) observations, made with the IRAM-30m telescope, towards the ram-pressure stripped tail northeast of NGC4388 in Virgo. HII regions found all along the tails, together with dust patches have been targeted. We detect molecular gas in 4 positions along the tail, with masses between 7x10$^5$ to 2x10$^6$ M$_\odot$. Given the large distance from the NGC 4388 galaxy, the molecular clouds must have formed in situ, from the HI gas plume. We compute the relation between surface densities of star formation and molecular gas in these regions, and find that the star formation has very low efficiency. The corresponding depletion time of the molecular gas can be up to 500 Gyr and more. Since this value exceeds a by far Hubble time, this gas will not be converted into stars, and will stay in a gaseous phase to join the intracluster medium.Read less <