Hello, I am new to drones and have very limited knowledge on how they communicate between the receiver and the flight controller. 

Currently I was given a AT9S Pro controller and was wondering if the R9DS receiver would work the Mamba MK4 F722. I do know that the mamba supports Sbus and that the R9DS also has support for it too. However, I am not 100% sure that if it would work. Anything helps!

I've not personally used any RadioLink equipment, but according the documentation for the R9DS receiver it does make use of the standard SBUS protocol so there is no reason that it shouldn't work with the Diatone Mamba F722 MK4 FC. It will just be like wiring up and configuring any other SBUS capable receiver to that FC, so just follow the wiring recommendations in the FC manual for the Mamba MSR receiver (minus the S,Port connection) and it should work just fine.

If you're going to be using Betaflight 4.4.x or later then don't forget to ensure that you include the "SBUS" Radio Protocol option in the Build Configuration section when flashing firmware to the FC.