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We validate the COVMOS method introduced in Baratta et al. (2019) allowing for the fast simulation of catalogues of different cosmological field tracers (e.g. dark matter particles, halos, galaxies, etc.). The power spectrum and one-point probability distribution function of the underlying tracer density field are set as inputs of the method and are arbitrarily chosen by the user. In order to evaluate the validity domain of COVMOS at the level of the produced two-point statistics covariance matrix, we choose to target these two input statistical quantities from realistic $N$-body simulation outputs. In particular, we perform this cloning procedure in a $Λ$CDM and in a massive neutrino cosmologies, for five redshifts in the range $z\in[0,2]$. First, we validate the output real-space two-point statistics (both in configuration and Fourier space) estimated over $5,000$ COVMOS realisations per redshift and per cosmology, with a volume of $1\ [\mathrm{Gpc}/h]^3$ and $10^8$ particles each. Such a validation is performed against the corresponding $N$-body measurements, estimated from 50 simulations. We find the method to be valid up to $k\sim 0.2h/$Mpc for the power spectrum and down to $r~\sim 20$ Mpc$/h$ for the correlation function. Then, we extend the method by proposing a new modelling of the peculiar velocity distribution, aiming at reproducing the redshift-space distortions both in the linear and mildly non-linear regimes. After validating this prescription, we finally compare and validate the produced redshift-space two-point statistics covariance matrices in the same range of scales. We release on a public repository the Python code associated with this method, allowing the production of tens of thousands of realisations in record time. COVMOS is intended for any user involved in large galaxy-survey science requiring a large number of mock realisations.