Advice for a LiPo UPS
No, this won't work the way you want it to. The PMOS transistor won't be conducting until its gate voltage falls (at least) several volts. By the time that happens the voltage on your load is so low that the SIM800 module will not work properly.

The typical way to do this is to use two Schottky diodes. The cathodes of both are tied together and then to the load. The anode of one diode is tied to each of the voltage sources. Current will flow primarily from the source that is about 0.3V higher than the other, and there will never be a time when current does not flow from one of the sources.