Many thanks for all the replies! That was very helpful.
I found a site with a parts list for my model (Asus X756UX series). All SSD's there have the form factor
M.2 2280 SATA III 6Gb/s. So I took the risk and bought
this one.
I think I can use at least one screw at the rear end. One thing that amazes me is that all those pieces have 5 pins on the right and my connector has only 4.
@ computersavvy: The problem was that the manual says nothing about any hw specs. It seems that they don't want you to open it.
I was told that opening or installing linux will void the guarantee. What a nonsense.
I will report.