And working the other way around I use an Olympus FL-36R which is the same as Panasonics Fl360L and everything works fine.
don't be fooled by the term Wireless though, their un tethered triggering system is not wireless, its wire less, wireless implies that its triggered by radio waves, its not, its wire less, ie not connected by wires. The triggering system is optical so the flash has to be quite close to the camera and has to be in line of sight. Wireless triggered flash guns could be much further away from the trigger and could be out of sight, The could even be in a different room if needed, Optical wire less triggered systems are much more restrictive in their use.
I do wish everyone would use the correct terminology when discussing these things
I was told by Olympus and Panasonic reps at a photo exposition last year that Panasonic manufactures the FL-600R. It and the Panasonic FL360L only differ in cosmetics. The FL-600R will function remotely using the GX7 built in flash to send the control signals to the FL-600R. While this system is limited compared to wireless RF flash triggered system it does perform well. I was also told by the same reps that Panasonic Makes a lot of flashes for Canon and Nikon.