Hello
I need to change the italian translation of "K2 items” in search module options (the Joomla core one). I searched for override it, but I don't find any recurrence.
Please, how to?

For starters take a look in these files
en-GB.mod_k2_tools.sys.ini
en-GB.mod_k2_tools.ini
with your language prefix and see if what your looking for is in them
If so, create a languate override and change them there

Well, it is into it-IT.plg_search_k2.ini file
but the overrides form doesn't find it. So I manually override it on the server, but I suppose to lost the change at next update.

Try copying the file into the joomla language override folder and editing it. It may work
If that doesnt work try copying it into a template override directory, assign that template to the category, and test
Krikor or someone may chime in with a more definite answer, i havent tested this