I use it on the Sony Alpha 6000 with a manual FD 50mm. AF and aperture transmission are not an issue here. Actually, the adapter only keeps the lens at the right distance in front of the sensor. This works great and I think it will be the same with the Alpha 7III. 

Yes. I have the same lens and adaptor on my Sony a7ll and it works beautifully. The m42 is also known as the 'universal' mount as other 3rd party camera and lenses also used it. I own 6 other K&F e-mount adaptors to different lens makers (ltm, MD, CF/CD, Nikon) and they all are well built with a nice snug fit. Highly recommended. 

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I actually have not received this adapter yet. It's shipping from China. Don't think that was disclosed in the ad. However, I do not believe this is for the Pentax Q body rather for digital and film cameras that take the Pentax K mount in its many variations. So I'm expecting to be able to mount my Leica M mount lenses on my digital and film Pentax K mount cameras, no autofocus or relay of exposure information, only to be used with manual focus and exposure. 

Yes it should work with the sony a6000. As long as the ka lens has an aperture ring on the lens and is not solely dependent on receiving aperture control from the body, this adapter should work fine with ka lenses. To my knowledge, there are no sony e mount to k mount adapters with electronic coupling so no lens control through the body (meaning aperture and focus are fully manual).