Thanks for fast reply,
I asked support to WPML They’ll reply.
Probably you miss a part of my explanation. I excuse for its length but it includes some important details.
The WPML language Switcher in that position is not a menu..
So, that is not that part of the content of the documentation to take help from. I just say that to clarify that is not a good reference for other people that ask the same.
About possibile solution as I already wrote ( for other people looking for support):
-create a menu and place it as an object into the mobile header: it’s not a solution because to appear the menu needs almost one ‘real menu voice’ a part from the menu switcher.
– place a Custom Switcher using [wpml_language_selector_widget] adding to the header a text/html object, doesn’t show the switcher. Don’t ask me why, I’m just reporting
I’m wondering if it is good to have a language switcher with text there (there=the natural position in a usability prospective) and why there’s no way to eliminate text in easy way, if there’s 100% compatibility.
As soon I will find a solution, I will post here the wpml reply.
Regards

PS
Please, let me say that in any case, since it’s a reasonable (basic) request to have the language switcher there (it’s not a theme customisation), and it’s a usability need to exclude language text, I suggest to try the steps to get it and get the goal. Probably for me is a matter of much time, but for you (that create the theme and made it wpml compatible) a very fast job.
Thanks again