Please try following code
add_filter( 'fep_message_query_args', function( $args, $user_id ) {
if( ! empty( $args['s'] ) && ( $user = get_user_by( 'login', trim( $args['s'] ) ) ) ) {
$args['participant_query'][] = array(
'mgs_participant' => $user->ID,
);
unset( $args['s'] );
}
return $args;
}, 10, 2 );