This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
Socket communication is generally two-way communication. As long as a client is connected to the server, both sides can send and receive. Furthermore, if the server is properly multi-threaded, then both clients A and B can do so at the same time.