I had to do something like this once...
I created a class that inherits from application
and created, within it these methods to read and record the current Activity.
public class AppApplication extends Application
{
    private Activity mCurrentActivity = null;
    public Activity getCurrentActivity(){
        return mCurrentActivity;
    }
    public void setCurrentActivity(Activity mCurrentActivity){
        this.mCurrentActivity = mCurrentActivity;
    }
}
I also created a class that contained the base implementation of Activity’s
public class BaseActivity extends Activity{
    protected AppApplication application;
    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        requestWindowFeature(Window.FEATURE_ACTION_BAR);
        //faz o cast para o tipo da minha classe de Application
        application = (AppApplication)this.getApplicationContext(); 
    }
    @Override
    protected void onResume() {
        super.onResume();
        //cada vez que é criada ou é resumida a activity grava a activity atual
        //ou seja sempre vou ter a Activity atual "gravada"
        //você pode fazer guardar ao invés da instância da activity, grava uma TAG que identifica e grava em algum local, e na hora de abrir o app você ler deste local.
        application.setCurrentActivity(this); 
    }
}
I changed all my activitys to 
public class Exemplo extends BaseActivity {
    ...
}
and in the manifest add your Appapplication class
<application
            android:name=".Globais.AppAplication"
            android:icon=...
            android:label=...
            android:theme=...>
        <activity...
I know it’s not quite what you need, but I decided to share my experience, because when you don’t have anything. Something is very useful..
I hope I’ve helped!!
							
							
						 
You can save in sharedPrefferences the last screen of the user, implement a method and call it always in onDestroy(); If the user closes the app.. you can create a service that forces him to stay with the app open, but I think it’s kind of "dangerous".
– Carlos Bridi
@Carlosbridi, I think calling onDestroy is not a good idea... I would record onResume, so I understood, for example if the user takes the battery, will not be able to call onDestroy for example..
– Marco Giovanni
@Carlosbridi I tried to use sharedprefferences, but when I forcibly close sharedprefferences is clean and back to default. It seems some android bug I’ve even researched about...
– Mateus Carvalho