You can use conditional
eg.

add_filter( 'fep_menu_buttons', function( $menu ) {
    if ( isset( $_GET['fepaction'] ) && $_GET['fepaction'] == 'message_box' ){
    $menu['cus_button'] = array(
        'title'		=> __( 'Edit', 'front-end-pm' ),
	'action'	=> 'edit',
        'class'         => 'fep-button your_unique_class',
	'priority'	=> 15,
    );
    }
    return $menu;
});