In an inverter with RL load, how does an increase in output inductance result in decrease in the magnitude of the current?
If R and L are in series then increasing the inductance will clearly increase the load impedance and cause less current to flow. It's as basic as ohms law.

Load impedance = \$\sqrt{R^2+X_L^2}\$

Where \$X_L = 2\pi f L\$

If R and L are in parallel then the same happens - if L increases then the reactive current taken by that component reduces the overall current drawn from the inverter.