  In order to explain the variance of the solar rotation law during the
activity minima and maxima, the angular momentum transport by rotating
magnetoconvection is simulated in a convective box penetrated by an inclined
azimuthal magnetic field. Turbulence-induced kinetic and magnetic stresses {
and} the Lorentz force of the large-scale magnetic background field are the
basic transporters of angular momentum. Without rotation, the sign of the
magnetic stresses naturally depends on the signs of the field components as
positive (negative) $B_\theta B_\phi$ transport the angular momentum poleward
(equatorward). For fast enough rotation, however, the turbulence-originated
Reynolds stresses start to dominate the transport of the angular momentum flux.
The simulations show that positive ratios of the two meridional magnetic field
components to the azimuthal field reduce the inward radial as well as the
equatorward latitudinal transport,%by the rotating magnetoconvection which
result from hydrodynamic calculations. Only for $B_\theta B_\phi>0$ (generated
by solar-type rotation laws with an accelerated equator) does the
magnetic-influenced rotation at the solar surface prove to be flatter than the
nonmagnetic profile together with the observed slight spin-down of the equator.
The latter phenomenon does not appear for antisolar rotation with polar vortex
as well as for rotation laws with prevailing radial shear.
