You are getting a new HashMap, which is a copy of the original HashMap. The values in the new Map are the exact Objects in the original, but that should not be a problem because the types are Integer and String, which are both immutable.
There is a problem with your terminology, though. There is no such thing as a 'static HashMap' and you are not creating an instance of it. Rather, you have a static variable which points to a HashMap and you are creating a new copy of that HashMap.
I checked the string references in the debugger and they were different, so my method works
As Steve has already pointed out it wouldn't matter if the references were the same or not. Integer and String objects are immutable and so can't be edited, therefore, even if the user changes one of the values in the copy it won't affect the original in any way.