How to make 2 clients connect each other directly, after having both connected a meeting-point server?

I'm writing a toy meeting-point/relay server listening on port 5555 for two clients "A" and "B".

It works like this: every byte received by the server from the firstly-connected client A will be sent to the secondly-connected client B, even if they are not in the same network, and even if A and B don't know their respective IP:

A -----------> server <----------- B     # they both connect the server first
A --"hello"--> server                    # A sends a message to server
               server --"hello"--> B     # the server sends the message to B

This code is currently working:

# server.py
import socket, time
from threading import Thread
socket = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
socket.bind(('', 5555))
socket.listen(5)
buf = ''
i = 0

def handler(client, i):
    global buf
    print 'Hello!', client, i 
    if i == 0:  # client A, who sends data to server
        while True:
            req = client.recv(1000)
            buf = str(req).strip()  # removes end of line 
            print 'Received from Client A: %s' % buf
    elif i == 1:  # client B, who receives data sent to server by client A
        while True:
            if buf != '':
                client.send(buf)
                buf = ''
            time.sleep(0.1)

while True:  # very simple concurrency: accept new clients and create a Thread for each one
    client, address = socket.accept()
    print "{} connected".format(address)
    Thread(target=handler, args=(client, i)).start()
    i += 1

and you can test it by launching it on a server, and do two netcat connections to it: nc <SERVER_IP> 5555.

Now in the particular case where these two clients are in the same local network (example: using the same home router), this will be displayed on server when the 2 clients will connect to the server on port 5555:

('203.0.113.0', 50340) connected  # client A, router translated port to 50340
('203.0.113.0', 52750) connected  # same public IP, client B, router translated port to 52750

How can I then pass the information to client A and B that they can talk directly to each other without making the bytes transit via the server?

(in general and especially in the case where they are in the same local network)

from How to make 2 clients connect each other directly, after having both connected a meeting-point server?