USB Steering Wheel: Encoder instead of Analog Potentiometer, need help

Ok so I had an old cheap USB steering wheel laying around and it uses an analog potentiometer (10k) for the steering wheel. Since analog potentiometers are inaccurate, unreliable and have a limited turning angle of 270 degrees I want to replace it with an encoder like this one Ive measured the voltage that the pot uses and its about 4,6 volts. I know how to connect an encoder to an arduino and read the values but I dont know how to output them to the pin where the logic board reads the value of the original potentiometer. If possible I want to avoid replacing the board with the arduino Pro micro because i want the wheel to be finished as quickly as possible. Please help

You need to recreate an analog signal from a PWM output by using an RC filter.
Then be sure how the existing steering wheel input works and match the voltage range ( if that is how it works).

BTW a pot is usually good enough for a steering wheel control unless you want multiple turns of the wheel , you need to do the sums