Somewhere in your AsyncTask you’ll want to pass in your activity. Then you’ll save that reference in a weak reference. Then you can dereference and use it again in onPostExecute.
Class member:
WeakReference<Activity> weakActivity;
Somewhere in AsyncTask, probably either constructor or onPreExecute:
weakActivity = new WeakReference<Activity>(activity);
In onPostExecute:
Activity activity = weakActivity.get();
if (activity != null) {
// do your stuff with activity here
}