The input power of the motor, that is, the output power of the inverter and the input power of the inverter are isolated from each other through DC, so the power factor of the motor has no influence on the input of the inverter.
It is wrong to say that the inverter can improve the power factor of the motor to 1. Although the instantaneous power factor of the motor is affected by power supply voltage, motor load rate and power supply frequency, the power factor of the motor as an inductive load is always less than 1.