The unbounded dimension of orbital angular momentum of light has made it one of the most vital parameters to store, control and transport information in optical communication. Along with orbital angular momentum, frequency, polarization and intensity of light are also essential degrees of freedom for encoding and multiplexing data streams in optical and quantum information processing. Therefore, nonlinear generation and conversion of orbital angular momentum have attracted considerable attention in recent years. Here, we theoretically and experimentally demonstrate the nonlinear conversion of orbital angular momentum in atomically thin tungsten disulfide monolayer at both of the second- and third-harmonic frequencies of the fundamental vortex beam. Moreover, we also show that by taking advantage of the symmetry properties of the crystal, the intensity and polarization state of the converted nonlinear vortex beam can be precisely controlled and determined by the polarization state of the fundamental beam. Our results can have a direct implication in building atomically thin optical multiplexers, signal processors, and other prototypes in nonlinear optical conversion for future on-chip photonic circuits, quantum memory and computing devices. [ABSTRACT FROM AUTHOR]