push notification android do something when push app close arrives

Bruno, the reception of data in your class that extends from FirebaseMessagingServiceand that specifically occurs in onMessageReceived()is understood to be to generate a notification, this does not matter if the application is open or closed.

As for your method it can work without any problem, you do NOT need to specify any type of FLAG or use onNewIntent() :

   private void mostrarNotificacion(String title, String body) {

        Intent intent = null;
        if(body.equals("Login")){
            intent = new Intent(this, Login.class);
        }
        if(body.equals("AppIntro")){
            intent = new Intent(this, AppIntroGalery.class);

        }
        if(body.equals("Menu")){
            intent = new Intent(this, TabsActivity.class);
        }

        intent.setFlags(Intent.FLAG_ACTIVITY_CLEAR_TOP);
        PendingIntent pendingIntent = PendingIntent.getActivity(this, 0, intent, PendingIntent.FLAG_ONE_SHOT);

        Uri soundUri = RingtoneManager.getDefaultUri(RingtoneManager.TYPE_NOTIFICATION);

        NotificationCompat.Builder notificationBuilder = new NotificationCompat.Builder(this)
                .setContentTitle(title)
                .setContentText(body)
                .setAutoCancel(true)
                .setSmallIcon(R.mipmap.ic_launcher_round)
                .setSound(soundUri)
                .setContentIntent(pendingIntent);

        NotificationManager notificationManager = (NotificationManager) getSystemService(Context.NOTIFICATION_SERVICE);
        notificationManager.notify(0, notificationBuilder.build());

    }

For it to work properly you have to take into account these points:

1) You need to specify your activities inside your AndroidManifest.xml file

 ...  
        <activity android:name=".Login"/>
        <activity android:name=".AppIntroGalery"/>
        <activity android:name=".TabsActivity"/>
    </application>

...

2) The parameter bodymust specifically contain the text that you indicate in the comparison:

   if(body.equals("Login")){
   ...
   if(body.equals("AppIntro")){
   ...
   if(body.equals("Menu")){
   ...

3) The most important point is that using FCM it is received in a RemoteMessage and not a Bundle. You are showing the notification if remoteMessage.getNotification():

   if (remoteMessage.getNotification() != null) {
            Log.d(TAG, "Notificación: " + remoteMessage.getNotification().getBody());

            mostrarNotificacion(remoteMessage.getNotification().getTitle(), remoteMessage.getNotification().getBody());
        }

but it does not open the intenttowards the Activity because the value of remoteMessage.getNotification().getBody(), is not "Login", "AppIntro" or "Menu", you should check this point.

It is also important to change the code of the notification because if you received one previously that did not have bodythe same code that you have with value 0, then this would cause it not to open any Activity, I suggest you create a method to obtain a random value that will serve as code:

private int getRandomCode(){
    //Obtiene un valor entre 1000.
    Random rand = new Random();
    return rand.nextInt(1000 - 0 + 1);
}

and define this code in the intent:

 private void mostrarNotificacion(String title, String body) {

        int codigo = getRandomCode();

        Intent intent = null;
        if(body.equals("Login")){
            intent = new Intent(this, Login.class);
        }
        if(body.equals("AppIntro")){
            intent = new Intent(this, AppIntroGalery.class);

        }
        if(body.equals("Menu")){
            intent = new Intent(this, TabsActivity.class);
        }

       // intent = new Intent(this, TabsActivity.class);
        intent.putExtra("idScreen", 12);
        intent.setFlags(Intent.FLAG_ACTIVITY_NEW_TASK | Intent.FLAG_ACTIVITY_CLEAR_TASK);
        PendingIntent pendingIntent = PendingIntent.getActivity(this, codigo/*0*/, intent, PendingIntent.FLAG_UPDATE_CURRENT);

        Uri soundUri = RingtoneManager.getDefaultUri(RingtoneManager.TYPE_NOTIFICATION);

        NotificationCompat.Builder notificationBuilder = new NotificationCompat.Builder(this)
                .setContentTitle(title)
                .setContentText(body)
                .setAutoCancel(true)
                .setSmallIcon(R.mipmap.ic_launcher_round)
                .setSound(soundUri)
                .setContentIntent(pendingIntent);

        NotificationManager notificationManager = (NotificationManager) getSystemService(Context.NOTIFICATION_SERVICE);
        notificationManager.notify(codigo /*0*/, notificationBuilder.build());

 }

In this case, only the first notification will open one Activityin the application since, as I mentioned, the condition is that it bodyhas a value of "Login", "AppIntro" or "Menu", if you open one that does not meet this condition, it will simply open from the beginning.

I tell you that if you have the app closed it will not work that way, well I already tried it, what the firebase documentation recommends and that if it worked for me, is to send in the message data, the activity that I am looking for to open to When clicking on the notification and of course, the background color so that the icon does not look all white, I send them from php in this way, but it would apply to any other way of requesting it:

$msg = array(
                'title'        => 'miTitulo',
                'body'         => 'miAsunto',
                'icon'         => 'ic_notifi_icon',
                'sound'        => 'defaultSoundUri',
                'click_action' => 'miActivity',//Actividad que se abrirá al momento de hacer clic en la notificacion
                'color'        => '#3F51B5'
            );

$fields = array(
                    'to'=> '/topics/'.$this->topic, 
                    'notification'  => $msg
                );

$headers = array(
                    'Authorization: key=' . $this->apikey, 
                    'Content-Type: application/json'
                );


$ch = curl_init();
        curl_setopt( $ch,CURLOPT_URL, 'https://fcm.googleapis.com/fcm/send' );
        curl_setopt( $ch,CURLOPT_POST, true );
        curl_setopt( $ch,CURLOPT_HTTPHEADER, $headers );
        curl_setopt( $ch,CURLOPT_RETURNTRANSFER, true );
        curl_setopt( $ch,CURLOPT_SSL_VERIFYPEER, false );
        curl_setopt( $ch,CURLOPT_POSTFIELDS, json_encode( $fields ) );
        $result = curl_exec($ch );
        curl_close( $ch );

The subject in question is the click_action which is where you indicate which activity you want to open when you click on the notification. The color is used for when the icon remains blank, because when it is in the background or closed, it does not take the configuration of the firebase listener.

This works perfect when the app is closed or in the background.

REPOSITORIO con formulario php para envío de notificaciones push

Saludos

Bien una de las formas en hacer lo que tu quieres es obtener los datos desde la actividad principal que es la primera en abrirse. cuando la app esta cerrada por completo y te llega una notificación al hacer clic en la notificación esta ya te abre el intent principal con datos como Extras, entonces esos extras deberás obtenerlos de la siguiente forma en tu onResume

@Override
protected void onResume() {
    if(getIntent().getExtras() != null) {

        Bundle b = getIntent().getExtras();

        try {
            String actionType = b.getString("action");
            //aquí va tu código en el cual validas el tipo de dato
        } catch (Exception e) {
            e.printStackTrace();
        }
    }
}

Now you will ask yourself, for example, why I sent to get action, well as I asked you if you were using the Firebase console in the Custom Data section you can put actionas the Key and then the values ​​would be the ones you want to review Login AppIntroetc. This answer is more based on my experience receiving Push notification in FireBase With the App closed and doing an action according to what is received in the notification.

As an annex to my answer I send you the link of how you send the data when using FCM: Receive Messages