In my plugin I set up a button displaying a category list in a popup.

class Books extends Controller
{   
    public $implement = [
        'Backend.Behaviors.FormController',
        'Backend.Behaviors.ListController',
    ];  

    public $formConfig = 'config_form.yaml';
    public $listConfig = 'config_list.yaml';

    public $listWidget = null;
    public $searchWidget = null;

    public function __construct()
    {
        parent::__construct();

        $this->createSearchWidget();
        $this->createListWidget();
    }   

   ...

    public function createSearchWidget()
    {   
        $config = ['prompt' => 'backend::lang.list.search_prompt'];
        $this->searchWidget = $this->makeWidget('Backend\Widgets\Search', $config);
        $this->searchWidget->bindToController();
    }   

    public function createListWidget()
    {   
        $config = $this->makeConfig('$/codalia/bookend/models/category/columns.yaml');
        $config->model = new \Codalia\Bookend\Models\Category;
        $config->recordsPerPage = 10; 
        $config->showPageNumbers = true;
        $config->recordOnClick = 'selectCategoryItem(:id, \':name\');';

        $this->listWidget = $this->makeWidget('Backend\Widgets\Lists', $config);
        $this->listWidget->bindToController();
    } 

    public function onLoadCategoryList()
    {
        $this->vars['search'] = $this->searchWidget;
        $this->vars['modelList'] = $this->listWidget;
        return $this->makePartial('modal_category');
    }

   ...

}

in my partial:

<?= $search->render() ?>
<?= $modelList->render() ?>

So far so good, both the category list and the search box are displayed in my modal window.
But when I type something in the search box, the list is not filtered.
What can I do to connect the 2 widgets in order to have the searched word taken into account in the category list query ?

Look at ListController behavior, it does have a search widget linked to the list widget.

Good call ! The solution lies in the makeList() method.
It just needs to use the bindEvent() method.

public function createSearchWidget()
{
    $config = ['prompt' => 'backend::lang.list.search_prompt'];
    $this->searchWidget = $this->makeWidget('Backend\Widgets\Search', $config);
    $this->searchWidget->bindToController();

    /*  
     * Link the Search Widget to the List Widget
     */
    $this->searchWidget->bindEvent('search.submit', function () {
        $this->listWidget->setSearchTerm($this->searchWidget->getActiveTerm(), true);
        return $this->listWidget->onRefresh();
    });
}