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.
If you use RMI you do not have to do anything special for sending a HashMap across from one server to another.
However, the synchronization is a little tricky as the instance of HashMap will be different for the two JVMs you can not have a single lock monitor.
If you explain in detail by what do you mean by " keep it synchronized. ", we will be able to help more.