Three problems...

so after tests it seems that the native joomla menu module (the second one that points exactly on the same items than the accordeon menu) does not receive the active class at all. So the problem is not related to the accordeon module
now what is strange, is that you have published another menu that points to the same pages but with other items (IDs are different) and this menu has the active class...
This the only thing I can tell you to help you with this

What menu in the another menu that points to the same pages but with other items?
I see the identical ID in the same menu item of both menu (ck and joomla)...where you see the active class, in firebug? I see for example in "Ensalada" a li id "item-804" and a class "accordeonck item-804 level2" meanwhile joomla menu item have a li class "item-804". but this is for CK module difference...

yes now they are the same
but remember at the beginning. Per email I have asked you and you have changed it, this is the answer you have given

No, excuse me, it was the old menu. I had created a special menu for to join with pasta delivery.
Now I published the menu "Menu desplegable", that is the same of "Carta del ristorante". "Menu desplegable" is a normal joomla menu.

the other menu with items ID 783,784, etc works

where you see the active class, in firebug?

yes you should see it on the <li> element

I discovered.
It was because the menu items were directed to an external URL and not directly to "bill of fare" of phocamenu, ie directly to the content.
Thank you very much...!
Please tell me now why I do not see the icons and I can not give another letter size to the first menu item ...

it seems that no style for this is loaded. Are you sure that you have enabled the "use styles of the module" in the options ?