I think all implementations of Collection have a constructor, which takes another Collection and adds all the elements to the new object, like new ArrayList(someHashSet).
Speaking of Map type, we have a problem, since Map is not a Collection and it's entry needs two things - key and value, while Collections can provide only one element, so you have to populate a Map manually.
Most Collection classes have a constructor that take any other Collection. Even if they don't, each Collection has the addAll method. If the collection allows adding elements then you can create an empty collection, then call this method:
Map is more difficult since you want to convert a "1 dimensional" structure to a "2 dimensional" structure. What will the values for the keys be?
The other way around (Map to Collection) will be easier since Map has three Collection views (keySet(), values(), entrySet()) which already turn the Map into a Collection (well, kind of).
No, you can not convert a Collection to a Map, because it has an entirely different structure. You would have to do this manually, and even that takes some effort as you have to specify keys and values, not just values like in a Collection.
Life is full of choices. Sometimes you make the good ones, and sometimes you have to kill all the witnesses.