Thanks Kharis, I know everything is working fine with the child theme It is working from the minute zero, but you obviously didn’t understood my original question. I’ve not problems at all with my child theme. and my customization of the functions.php works as usual in many of my sites, nothing there to look at.
What I have asked originally is if I do some customization in the parent theme (i.e. I add some header image) if will be “replicated” or “cascaded” to the child theme (which I supposed will not happen). That’s “not working” and is ok because I’m almost 100% sure that those customizations are options associated to the current theme so will not be visible by its “descendants”.
Where I said “nothing working”? I said “it doesn’t preserve any of the configurations set to the parent theme as I supposed” and that’s ok, is how themes and sub-themes works, just tried to verify it with you.
Please close the issue because you just didn’t understood my question (perhaps because of my non native english) and everything works perfectly as advertised, your theme and my child theme.