how to access an object created in one stateful widget in another stateful widget in flutter

There are lots of ways to do this depending on your use case. Here are a few options:

1. You can expose the created object as public member of your State. Then use the currentState property of a GlobalKey in one State to get a reference to the other State. Now you can access the created object via the public member. (Note: This pattern limits the testability and encapsulation of your State, so use it sparingly.)
2. Both widgets can have a ancestor widget that extends InheritedWidget that they use to look up the created object.
3. Both widgets can be passed a model argument in their a constructor, such as a ValueNotifier. They can use this object to read and write the value.

If you go into more detail on your use case we can help you pick a pattern that makes sense.

Here is some code implementing option #1.

import 'package:flutter/material.dart';

void main() {
  runApp(new MyApp());
}

final key = new GlobalKey<MyStatefulWidget1State>();

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return new MaterialApp(
      home: new Scaffold(
        body: new Column(
          mainAxisAlignment: MainAxisAlignment.spaceAround,
          children: <Widget>[
            new MyStatefulWidget1(key: key),
            new MyStatefulWidget2(),
          ],
        ),
      ),
    );
  }
}

class MyStatefulWidget1 extends StatefulWidget {
  MyStatefulWidget1({ Key key }) : super(key: key);
  State createState() => new MyStatefulWidget1State();
}

class MyStatefulWidget1State extends State<MyStatefulWidget1> {
  String _createdObject = "Hello world!";
  String get createdObject => _createdObject;

  @override
  Widget build(BuildContext context) {
    return new Center(
      child: new Text(_createdObject),
    );
  }
}

class MyStatefulWidget2 extends StatefulWidget {
  State createState() => new MyStatefulWidget2State();
}

class MyStatefulWidget2State extends State<MyStatefulWidget2> {
  String _text="PRESS ME";

  @override
  Widget build(BuildContext context) {
    return new Center(
      child: new RaisedButton(
        child: new Text(_text),
        onPressed: () {
          setState(() {
            _text = key.currentState.createdObject;
          });
        },
      ),
    );
  }
}