PrestaShop will only copy automatically to the override folder the PHP file of the same name of the module. Sometimes you need to override other files of a module - with this code you can that in your own custom module.

prestashop_move_overrides.php

<?php
// The path to the /override/modules folder in your custom module
$module_path = _PS_ROOT_DIR_ . DIRECTORY_SEPARATOR . 'modules' . DIRECTORY_SEPARATOR . $this->name .
    DIRECTORY_SEPARATOR . 'override' . DIRECTORY_SEPARATOR . 'modules';

// The path to the PrestaShop override folder
$override_path = _PS_ROOT_DIR_ . DIRECTORY_SEPARATOR . 'override' . DIRECTORY_SEPARATOR . 'modules';

// Add an entry to the array for all of the overrides that you want to be copied to the override folder:
$files = array(
    // override 1
    DIRECTORY_SEPARATOR . 'module_name' .
    DIRECTORY_SEPARATOR . 'folder_name' .
    DIRECTORY_SEPARATOR . 'file_name.php',
    // override 2
    DIRECTORY_SEPARATOR . 'module_name' .
    DIRECTORY_SEPARATOR . 'folder_name' .
    DIRECTORY_SEPARATOR . 'file_name.php',
);

foreach ($files as $file) {
    $from = $module_path . $file;
    $to = $override_path . $file;
    // Create directories that need creating
    $path = pathinfo($to);
    if (!file_exists($path['dirname'])) {
        if (!mkdir($path['dirname'], 0755, true)) {
            // Folder creation failed
            return false;
        }
    }
    // Copy file
    if (!copy($from, $to)) {
        // File copy failed
        return false;
    }
}

// All done
return true;