Dave,
Here is the process I have used successfully to upgrade the receiver firmware using a X10s and servo extension wire to the receiver.
1) Goto the FrSky website to download the latest Rx firmware, which for your receiver would be at
https://www.frsky-rc.com/rx4r/
2) unzip the file, selecting the correct firmware version, then copy the *.frk file to your SD card. Create a folder on your SD card named "FIRMWARE" and place the .frk file in this directory, then insert the SD card into your X10s.
3) Connect your receiver via a servo extension cable from the S.Port on the receiver to the connector on the back of the X10s radio under the rubber cover, it is the center connector. The critical piece of information is the correct polarity, below is an image with the correct orientation, make sure this is correct. The left side is the signal (yellow wire) and the right side is the ground wire (brown wire).
4) On the X10 menu, press the SYS button, select UPDATE. The firmware file name should be shown on the large screen to the left, select it with the right scroll knob, then select UPDATE. The process takes about a minute or two.
The key challenge, I had was knowing the correct orientation of the servo wire on the X10s as all of my servo cables are not keyed and I found no documentation for this info. I used a DVM to measure the voltage on each pin, which allowed me to determine which was the ground pin (right or left) as the center is always power
I hope this helps, as it is a simple process, once you know how to do it. I would defer to others for the correct firmware version to select, as I see there are many options.
Cheers,
Terry