In first activity, there is empty ListView and Button. 
When I press button, it starts second activity that has ListView of categories. 
After I click into one of listElements it will start third activity that has ListView with elements that are belong to my chosen category.
When I choose element of third ListView it must send me back to first activity, where my chosen element is added to my empty ListView
Use Intent.FLAG_ACTIVITY_FORWARD_RESULT like this:
FirstActivity should start SecondActivity using startActivityForResult().
SecondActivity should start ThirdActivity using this:
Intent intent = new Intent(this, ThirdActivity.class);
intent.addFlags(Intent.FLAG_ACTIVITY_FORWARD_RESULT);
startActivity(intent);
finish();
This tells ThirdActivity that it should return a result to FirstActivity.
ThirdActivity should return the result using
setResult(RESULT_OK, data);
finish();
At that point, FirstActivity.onActivityResult() will be called with the data returned from ThirdActivity.
Though I'd implore you to change your architecture design, it is possible to do it like this:
File ActivityOne.java
...
startActivityForResult(new Intent(this, ActivityTwo.class), 2);
...
@Override
public void onActivityResult(int requestCode, int resultCode, Intent data) {
    if(resultCode == RESULT_OK && data != null) {
        //Collect extras from the 'data' object
    }
}
...
File ActivityTwo.java
...
startActivityForResult(new Intent(this, ActivityTwo.class), 3);
...
@Override
public void onActivityResult(int requestCode, int resultCode, Intent data) {
    if(resultCode == RESULT_OK && data != null) {
        setResult(resultCode, data);
        finish();
    }
    setResult(RESULT_CANCELLED);
}
...
File ActivityThree.java
...
//Fill the Intent resultData with the data you need in the first activity
setResult(RESULT_OK, resultData);
finish();
...
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