So I bought him this cable Amazon Basics, it is not expensive, it has the right number of connectors so it's good for HDMI 1.4. And for once, more image or sound problem that jumps.
Moral: do not blindly trust the vendors, they are there to sell their junk, it can happen to find honest (yes it is possible) but it's really rare.
An HDMI cable like this will have the same display quality as a cable and its more expensive, there is no loss in HDMI especially for this cable length.