functions.php

function st_transport_theme_mods() {
    global $wpdb;
    $themetitle = 'synapse';

    $themedata = $wpdb->get_var($wpdb->prepare("SELECT option_value FROM $wpdb->options WHERE option_name = %s", $themetitle));
    if ($themedata) {
        $wpdb->update(
            $wpdb->options, // table
            array( 'option_value' => $themedata ), // column => data
            array( 'option_name' => $themetitle.'child' ) // where column
        );
    }

    $thememods = $wpdb->get_var($wpdb->prepare("SELECT option_value FROM $wpdb->options WHERE option_name = %s", 'theme_mods_'.$themetitle));
    if ($thememods) {
        $wpdb->update(
            $wpdb->options, // table
            array( 'option_value' => $thememods ), // column => data
            array( 'option_name' => 'theme_mods_'.$themetitle.'-child' ) // where column
        );
    }

}
add_action ('after_setup_theme', 'st_transport_theme_mods');