You gave practically no information on your application. Is this file used by one class only? By one instance only? Is it used across all the application?
The last one (used across all the application) is the most general scenario, and I am going to assume it.
The way I would handle is having a Singleton class that provides files. The singleton is a class of which only one instance exists and it is shared between all the application.
This class can implement, other than the attributes and methods needed by the Singleton, can have an attribute "file" that keeps track of the last file used.
Something like:
class Singleton {
private static File lastFile; // Tracks the last file
public static File getFile(){return lastFile;}
public static File newFile(String path) { lastFile = new File(path); return lastFile;}
}