Before I called the method
Crashlytics.getInstance().core.logException(new Exception("..."))
Do I need to initialize Crashlytics like this
Fabric.with(this, new Crashlytics());
though I've initialized in the main screen?
You should initialize Crashlytics on your application class on the onCreate() method. That way all the fatal exceptions are caught by default and when creating a log you only need to call the
Crashlytics.getInstance()
every time you need it