public static Map<Integer, List<Integer>> stuff(arguments) {
HashMap<Integer, List<Integer>> map = new HashMap<>();
method(map, otherVariables);
return map;
}
public static void method(HashMap map, otherVariables) {
map.put(things);
}

So... You know how to return a map from a method. Then why do you create the map outside the method and make it an argument that does not get returned, making it confusing because the map gets created empty, given to a different method, then returned, making it look like you're returning an empty map...
...instead of just creating it inside the called method, returning it and assigning it to a map in the calling method? Even if you think that would create another map (it doesn't), the compiler is intelligent and can optimise that away.