The phone is clean, I have only transferred the files to the storage via cable, than rebooted to recovery, selected install, selected the zip and the error pops out. There is not much more I can do.

Edit

Trying it with ADB sideload and it also gave:
Updater process ended with error 7

Edit 2:

FIXED

Just as suspected - latest TWRP was a bad idea. I have used 3.2.1.1 and it worked. Installing Sailfish at this very moment