can you move the java installation to another directory?

There's a registry key below HKEY_LOCAL_MACHINE\SOFTWARE\JavaSoft\Java Runtime Environment which is looked up by %windir%\system32\java.exe and others, like probably your browser. Just have a look with regedit - the keys and values should be obvious, or have a look at Deploying the JRE on Windows for JDK 1.6.