First save the position of selected data from spinner in a String variable,

int positionOfSelectedDataFromSpinner;

spinner.setOnItemSelectedListener(new AdapterView.OnItemSelectedListener() {

    @Override
    public void onItemSelected(AdapterView parent, View view, int position, long id) {
       positionOfSelectedDataFromSpinner= position;
}
Then on button click send intent to Another activity with putExtra

Intent i = new Intent (this, activity2.class);

i.putExtra("position", positionOfSelectedDataFromSpinner);
startActivity(i);
get int from getIntent in another activity

Intent intent = getIntent();
int positionToShowToSpinner = intent.getStringExtra("position");
then set the position to spinner

spinner.setSelection(positionToShowToSpinner);
I think this my solve your problem.