Search template suggestions from a module
Thanks to the comments from @AlexGill and @Beebee I was able to figure out what's the actual suggestion name for my template file. Here's how I solved it:

&lt;?php

function history_search_theme()
{
    return array(
        'search_result__history_search' =&gt; array(
            'template' =&gt; 'search-result--history_search',
            'path' =&gt; drupal_get_path('module', 'history_search'),
            'base hook' =&gt; 'search_result',
        ),
    );
}