You can apply the List.addAll() method. It allows a Collection as an argument, and your set is a Collection.
List<String> mainList = new ArrayList<String>();
It is simple to see that if you want to beget a Map with Lists as values, to produce k distinct values, you need to generate k different lists.
Thus: You cannot bypass creating these lists at all, the lists will be created.
Set your Map as a
Map<String,Set> or Map<String,Collection> alternatively, and just enter your set.