Limit varieties of $J$-trivial monoids and their subvarieties are generated by monoids of the form $M_{\tau}(W)$

We show that limit varieties of monoids recently discovered by Gusev, Zhang and Luo and their subvarieties are generated by monoids of the form $M_\tau(W)$ for certain congruences $\tau$ on the free monoid. The construction $M_\tau(W)$ is a generalization of widely used Dilworth-Perkins construction.