how is it possible that an inverter absorb reactive power
Refer to the drawing below. In order to accommodate an inductive load, an inverter must have a capacitor with enough capacitance to store the energy received from the load during one half-cycle of the output waveform. The inverter switching elements must have anti-parallel diodes to carry current in the direction opposing the current from the DC supply.

The current between the DC supply and capacitor combination to the H-Bridge inverter will be DC with some AC ripple current. The ripple current is the reactive component of the current in the load it transfers energy back and forth between the inductance of the load and the capacitance in the inverter.