MainActivity.java

import android.os.Bundle;
import android.support.annotation.NonNull;
import android.support.v4.app.FragmentTransaction;
import android.support.v7.app.AppCompatActivity;

import java.util.ArrayList;
import java.util.List;

public class MainActivity extends AppCompatActivity implements Messenger {

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);
        FragmentTransaction transaction = getSupportFragmentManager().beginTransaction();
        transaction.add(R.id.activity_main, ReceiverFragment.newInstance(), ReceiverFragment.class.getCanonicalName());
        transaction.addToBackStack(ReceiverFragment.class.getCanonicalName());
        transaction.commit();
    }

    private List<MessengerListener> messengerListeners = new ArrayList<>();

    @Override
    public void addListener(@NonNull MessengerListener listener) {
        messengerListeners.add(listener);
    }

    @Override
    public void removeListener(@NonNull MessengerListener listener) {
        messengerListeners.remove(listener);
    }

    @Override
    public void sendMessage(@NonNull String message) {
        for (MessengerListener listener : messengerListeners)
            listener.acceptMessage(message);
        getSupportFragmentManager().popBackStack();
    }

    @Override
    public void openSender() {
        FragmentTransaction transaction = getSupportFragmentManager().beginTransaction();
        transaction.replace(R.id.activity_main, SenderFragment.newInstance(), SenderFragment.class.getCanonicalName());
        transaction.addToBackStack(SenderFragment.class.getCanonicalName());
        transaction.commit();
    }
}

Messenger.java

import android.support.annotation.NonNull;

public interface Messenger {
    void addListener(@NonNull MessengerListener listener);

    void removeListener(@NonNull MessengerListener listener);

    void sendMessage(@NonNull String message);

    void openSender(); //не обязательно использовать, открывайте это для только открытия нового фрагмента
}

MessengerListener.java

import android.support.annotation.NonNull;

public interface MessengerListener {
    void acceptMessage(@NonNull String message);
}

ReceiverFragment.java

import android.content.Context;
import android.os.Bundle;
import android.os.Handler;
import android.support.annotation.NonNull;
import android.support.annotation.Nullable;
import android.support.v4.app.Fragment;
import android.view.LayoutInflater;
import android.view.View;
import android.view.ViewGroup;
import android.widget.TextView;

public class ReceiverFragment extends Fragment implements MessengerListener {
    private Messenger mListener;

    private TextView textView;
    private String message;

    public ReceiverFragment() {
        // Required empty public constructor
    }


    public static ReceiverFragment newInstance() {
        return new ReceiverFragment();
    }

    @Override
    public View onCreateView(LayoutInflater inflater, ViewGroup container,
                             Bundle savedInstanceState) {
        // Inflate the layout for this fragment
        return inflater.inflate(R.layout.fragment_receiver, container, false);
    }

    @Override
    public void onViewCreated(View view, @Nullable Bundle savedInstanceState) {
        super.onViewCreated(view, savedInstanceState);
        textView = (TextView) view.findViewById(R.id.tvReceiptText);
        if (message != null) textView.setText(message);
        openSenderFragment();
    }

    private void openSenderFragment() {
        new Handler().postDelayed(() -> mListener.openSender(), 3000);
    }

    @Override
    public void onAttach(Context context) {
        super.onAttach(context);
        if (context instanceof Messenger) {
            mListener = (Messenger) context;
            mListener.addListener(this);
        } else {
            throw new RuntimeException(context.toString() + " must implement Messenger");
        }
    }

    @Override
    public void onDetach() {
        super.onDetach();
        message = null;
        mListener.removeListener(this);
        mListener = null;
    }

    @Override
    public void acceptMessage(@NonNull String message) {
        this.message = message;
        if (textView != null) textView.setText(message);
    }
}

SenderFragment.java

import android.content.Context;
import android.os.Bundle;
import android.support.annotation.Nullable;
import android.support.v4.app.Fragment;
import android.view.LayoutInflater;
import android.view.View;
import android.view.ViewGroup;
import android.widget.EditText;

public class SenderFragment extends Fragment {
    private Messenger mListener;
    private EditText editTextMessage;

    public SenderFragment() {
        // Required empty public constructor
    }

    public static SenderFragment newInstance() {
        return new SenderFragment();
    }

    @Override
    public View onCreateView(LayoutInflater inflater, ViewGroup container,
                             Bundle savedInstanceState) {
        return inflater.inflate(R.layout.fragment_sender, container, false);
    }

    @Override
    public void onViewCreated(View view, @Nullable Bundle savedInstanceState) {
        super.onViewCreated(view, savedInstanceState);
        editTextMessage = (EditText) view.findViewById(R.id.etMessage);
        view.findViewById(R.id.btSend).setOnClickListener(v -> onButtonPressed());
    }

    public void onButtonPressed() {
        if (mListener != null) {
            mListener.sendMessage(editTextMessage.getText().toString());
        }
    }

    @Override
    public void onAttach(Context context) {
        super.onAttach(context);
        if (context instanceof Messenger) {
            mListener = (Messenger) context;
        } else {
            throw new RuntimeException(context.toString() + " must implement Messenger");
        }
    }

    @Override
    public void onDetach() {
        super.onDetach();
        mListener = null;
    }
}