Save in my custom admin page and redirect to the saved object

You can call them with $last_item = $wpdb->get_row( "SELECT * FROM $wpdb->wp_puzzle ORDER BY your_table_id DESC LIMIT 1", ARRAY_A ); and put manualy every item in your inputs at the form

public function puzzle_manager(){
            global $wpdb;

            $file = file_get_contents('puzzle_manager.php', FILE_USE_INCLUDE_PATH);
            if($file == false){
                echo 'file not found';
            }
            else{
                echo $file;
            }

    $last_item = $wpdb->get_row( "SELECT * FROM $wpdb->wp_puzzle ORDER BY your_table_id DESC LIMIT 1", ARRAY_A  );

    if(!empty($last_item)){
    echo '<pre>';
    print_r_($last_item);
    //you must put manualy every $last_item value in your form, example $last_item['puzzle_title'] in puzzle_title input
    echo '</pre>';
    }

            $default = array(
            'puzzle_title' => '',
            'image' => '',
            'rows' => '',
            'cols' => '',
            'timer' => '',
            'movements_counter' => '',
            'original_button' => '',
            'numbers_button' => '',
            );

            $item = shortcode_atts( $default, $_REQUEST );
            $wpdb->insert( 'wp_puzzle' , $item );
        }