The photo of the conector shows a mono plug. Most wireless mic systems are not stereo, and I cannot comment on this by the photo, but I suspect it is mono as well.
If you are seeing the signal on both channels of the recording software, you could still be recording in mono--but just putting the same signal on both channels.
Check out the link I provided for recording your own CD, go through the instructions step-by-step, and you should not have a problem recording.
Good Luck,
Gary
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Travlin' Easy
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PSR-S950, TC Helicon Harmony-M, Digitech VR, Samson Q7, Sennheiser E855, Custom Console, and lots of other silly stuff!
K+E=W (Knowledge Plus Experience = Wisdom.)