Mockito - Trigger mocked method when passed list of certain parameters

Question

Consider following stub :

class InformationProvider{
    private FileAccessor; //custom interface, works like readable DAO, but on files. 

    public List<Information> getInformation (Collection<String> identifiers){
    List<Information> infoList = getInformationFromMemory(identifiers); 
    List<String> remaining = getListofIdsNotInMemory(identifiers, infoList); //looks up which IDs need to be searched in files.
    infoList.addAll(fileAccessor.getInformation(remaining));
    return infoList;
    }
}

I am writing a unit test for the provider. My idea was like following:

class InformationProviderTest{
    InformationProvider infoprovider = new InformationProvider();
    List<String> idsMemory = Arrays.asList("AAA", "BBB");
    List<String> idsFile = Arrays.asList("CCC", "DDD");
    @Mock
    FileAccessor fa;

    @Before
    public void setUp(){
    //All the necessary mock initialization and constructors and stuff
    infoprovider.setFileAccessor(fa);
    }

    @Test
    public void correctDataAllocationTest(){
    List<Information> requiredResult = buildInformation("AAA","BBB","CCC","DDD"); //Prepares Information objects for IDs "AAA","BBB","CCC" and "DDD" 
    List<Information> infoFromFile = buildInformation("CCC","DDD");

    Mockito.when(fa.getInformation(idsFile)).thenReturn(infoFromFile);

    infoProvider.getInformation(Arrays.asList("AAA","BBB","CCC","DDD"));
    //Asserts and stuff
    }

In my case, the method fa.getInformation is never called with List idsFile, because the actual list used as a parameter is created new inside the InformationProvider. Both lists do contain the same strings though, "CCC" and "DDD".

How do I make Mockito to match them? All the tutorials I found were dealing only with either objects or used anyList(). Using anyList() actually does the matching, but then loses the information about the IDs. I need to be sure that when called with other IDs, this method returns nothing, something along the lines of (afaik non-existing) "anyListContaining(<Collection>)".

I am also limited to using Mockito library.