I have NOT upgraded the receiver firmware as the version I’m running on the actual handheld did not require that.
What problem are you encountering?
When I try to install firmware for RX Remote Update Tool displays the message “download the correct firmware version.” I’ve tried all firmware versions, but the result is the same. The remote itself is running the latest firmware version.
Wish I could provide some guidance but not having done this myself it wouldn’t be credible.
I assume this is the version you are trying to get working
Maybe install the version before this one and if successful try the newer version again.
Firmware updates have always been potentially troublesome. 
I’ve done all updates. There both an RX file and a TX file. Use the RX file. Follow the steps described in the manual, and you should be fine with the firmware tool from Flipsky. You have to get the receiver in IAP mode too.
I followed the documentation. First, I flashed the remote. Then I switched the receiver to IAP mode. No results. What firmware version do you have for your remote?
I already wrote that I tried to use all existing firmware versions
Im on the 1.1.3. Same for the receivers. Weird that it does not work for you. Had no issues with both remotes. If you are 100% you followed the correct procedure described in detail in the newest manual (within the 1.1.3. folder), then I suggest you talk to flipsky. Both remotes for me had no issues.