First you start by opening the donor controller up.
Then you have to remove the chip.
Then you will set it on top of the other chip, and solder all the wires from the top chip down to the lower chip except for pin #'s 1, 17, and 18.. For a pinout of what pins do what, look at this file.
Then you should add 100 ohm resistors to the 3 wires that are connecting to the chips (I'm not sure if these are necessary, they were on the original board, so to be safe, these should probably be added).
Then solder the orange wire (clock) to pin 17, the brown wire (reset/latch) to pin 18, and the yellow wire (data) to pin 1, then the rest of the wires to their corresponding pins, and put it back together. You can fit both wires out the normal hole out of the controller casing. Then test it, and you should have control of both systems by using only one controller.
Note: I don't know that all 3 of those pins are needed to be separated for the other controller, it may be possible that only one or two of them need to be.