On the server side, message forwarding functionality is already implemented from prior work. The server only needs to route incoming messages to the inetnded recipient specified in the message envelope:

if (message.getType().equals(MessageType.COMMON_MESSAGE)) {
    // Get the active connection thread for the receiving user
    ClientConnectionThread targetClient = ConnectionManager.getClientThread(message.getReceiver());
    ObjectOutputStream objectOut = new ObjectOutputStream(targetClient.getSocket().getOutputStream());
    // Transmit the full message object to the recipient
    objectOut.writeObject(message);
}

After the client reecives the message packet from the server, it broadcasts the message data to the chat UI activity:

// Broadcast incoming message content to the chat activity
Intent broadcastIntent = new Intent("com.example.im.message_received");
String[] messageData = new String[]{
    incomingMessage.getSender(),
    incomingMessage.getContent(),
    incomingMessage.getSendTimestamp()
};
broadcastIntent.putExtra("incoming_message", messageData);
context.sendBroadcast(broadcastIntent);

The conversation list activity registers a broadcast receiver to process incoming messages:

public class ConversationListActivity extends Activity {
    ListView conversationListView;
    List<RecentConversation> recentConversations = new ArrayList<>();

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        requestWindowFeature(Window.FEATURE_NO_TITLE);
        setContentView(R.layout.activity_conversation_list);
        // Register broadcast receiver for new incoming messages
        IntentFilter messageFilter = new IntentFilter(); 
        messageFilter.addAction("com.example.im.message_received");
        registerReceiver(new IncomingMessageReceiver(), messageFilter);
    }

    public class IncomingMessageReceiver extends BroadcastReceiver {
        @Override
        public void onReceive(Context context, Intent intent) {
            String[] messageInfo = intent.getStringArrayExtra("incoming_message");
            String sender = messageInfo[0];
            String content = messageInfo[1];
            Toast.makeText(context, "New message from [" + sender + "]: " + content, Toast.LENGTH_SHORT).show();
            // Update the recent conversation list with the new message
        }
    }
}