It appears that the router board is running at 3.3V, so assuming that the serial output from it is at that level, you just need a logic level shifter between it and the PIC.
To connect the Router-TX to the PIC-RX, an easy way to shift the level is to use a 74LS04 logic chip. It's a hex inverter and will will detect anything above 2V as high input, so will work from the 3.3V signal. Power the 74LS04 from your 5V, connect an inverter input to the Router-TX, and the inverter's output to the input of another inverter. Then the output of that inverter (so the signal is now at 5V, and back to high for a high input) to the PIC-RX.
If you need to connect the PIC-TX to the router-RX to talk back to the router, then you can just use two resistors to drop the 5V to 3.3V. Connect the PIC-TX to a 1.8K resistor, to the other side of that resistor connect a 3.1K resistor, and connect the other side of that to ground. Then connect the middle of the resistors to the Router-RX.