What you want is called TaskStackBuilder.
Here you must create an intent that will move to SpecificPhotoActivity:
    Intent action = new Intent(context, SpecificPhotoActivity.class);
    PendingIntent pendingIntent = TaskStackBuilder.create(context)
            .addNextIntentWithParentStack(action)
            .getPendingIntent(0, PendingIntent.FLAG_UPDATE_CURRENT);
To correctly specify the action stack, you must provide android:parentActivityNameinside the manifest file:
<application ...>
    <activity android:name=".SpecificPhotoActivity"
        android:parentActivityName=".PhotosActivity"/>
</application>
, SpecificPhotoActivity PhotoActivity, TaskStackBuilder , , "Back" SpecificPhotoActivity.
:
    NotificationManager manager = (NotificationManager) getSystemService(NOTIFICATION_SERVICE);
    Notification notification = new NotificationCompat.Builder(this)
            .setContentTitle(...)
            .setContentText(...)
            .setSmallIcon(...)
            .setContentIntent(pendingIntent)
            .build();
    manager.notify(NOTIFICATION_ID, notification);
SpecificPhotoActivity. "", PhotosActivity.
, . , , . , :
    PendingIntent pendingIntent = null;
    if (authorized) {
        Intent action = new Intent(context, SpecificPhotoActivity.class);
        pendingIntent = TaskStackBuilder.create(context)
                .addNextIntentWithParentStack(action)
                .getPendingIntent(0, PendingIntent.FLAG_UPDATE_CURRENT);
    } else {
        Intent action = new Intent(context, IntroActivity.class);
        action.putExtra("photos_flow", true);
        pendingIntent = PendingIntent.getActivity(context, 0, action, 0);
    }
, IntroActivity :
    void onAuthorized() {
        if(getIntent().getBooleanExtra("photos_flow", false)) {
            
            Intent[] intents = new Intent[]{new Intent(this, PhotosActivity.class), new Intent(this, SpecificPhotoActivity.class)};
            startActivities(intents);
            finish();
        }
    }