As i drive a Main domain and a subdomain,
to enable visitors to search and find contents pubblished in both sites i set a google custom search who i installed with mentioned plugin in the sidebars of both sites.

Now i would like to add the php row code for calling the plugin:

<?php display_search_box($display_results_option); ?>

inside the BFA Atahulpa header in the same place where the theme put it own searching box ( off couse the Atahualpa searching box is disabled).

Could please explain me how to do, e.g.: where to put the code and how?

Main domani runs 3.4.9
and the subdomain runs Atahualpa 3.5.3.

Thanks!

In those versions you could wrap the code in a div with an id and put it various places in the theme options and then position with CSS. If you are planning on upgrading the theme you could add a New Widget area to those same places and then add the code to a php aware widget and again position with CSS.