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//Na view original

Intent i = new Intent(YourCurrentActivity.this, YourNextActivity.class);
String str = yourEditText.getText().toString();
i.putExtra("edittextvalue" , str);
startActivity(i);

//Na outra view
Bundle extras = getIntent().getExtras(); 
String myEtText;

if (extras != null) {
  myEtText = extras.getString("edittextvalue");
  yourTextView.setText(myEtText);
}