First of all, step 6 proved to be step 5 and vice versa. About step 7, I downloaded and installed the latest firmware to the device. Proved to be useless, but anyway.
Second, I installed the full driver package via a usb cable connection. So far so good. Opened the HP 4670 series app, the printer was functioning normally, engaging the color management.

I then opened the HP 4670 Series desktop app, and requested a new connection.

I clicked on wireless connection, then next.

Chose the right wireless printer (needless to show a screenshot, I have only one). Let the app install its' drivers and complete the process. I chose not to activate a proxy connection (since I don't know what that is). I then tried to print a pdf file in
color, using the wireless printer connection. Again, no color management.
Nothing seems to work. I have to add that the same process was followed on an HP laptop. The color management works fine there.
I really don't know what else to do.