In your onFinish overriden on StartActivity method just do:
@Override
public void onFinish() {
getSharedPreferences("APP", MODE_PRIVATE).edit().putInt("SOME_IDENTIFIER", score).commit();
Intent i = new Intent(getApplicationContext(), ScoreActivity.class);
startActivity(i);
}
And then on ScoreActivity onCreate method:
@Override
protected void onCreate(Bundle savedInstanceState) {
super.onCreate(savedInstanceState);
setContentView(R.layout.activity_score);
textFinal = (TextView)findViewById(R.id.textFinal);
int defaultValue = 0;
int score = getSharedPreferences("APP", MODE_PRIVATE).getInt("SOME_IDENTIFIER", defaultValue);
textFinal.setText(score);
}