Second and most efficient approach is using ThreadLocal class. You can set object in first method to this class by this:
Now in third method you can get this object using this:
Usually this approach is used with objects which are current request's context related e.g. FacesContext object is the key object in JSF and is required to use it anywhere in the request. so JSF creates instance of FacesContext in each request and set it to ThreadLocal. and then later on returns it from ThreadLocal.