Hi, the Phoenix dongle only works with Phoenix (it's deliberate designed so by Phoenix).
I'm not familiar with the JR transmitters myself but chances are you might get it working with a universal USB simulator dongle such as a "22 in 1" simulator cable that can be found in various places.
If that doesn't work out for you, you might get it working using the Smartpropoplus method mentioned in the manual.
(Sorry for the late reply, I must have somehow missed your post earlier).