While partitioning the elements in a list using GatherBy, can I correspondingly partition the elements of an unrelated list?

If we have a list like the following:

list1 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12};

And we use GatherBy to subpartition is according to a test function

GatherBy[list1, Mod[#, 3] &]

We have as an output for this example {{1, 4, 7, 10}, {2, 5, 8, 11}, {3, 6, 9, 12}}. See Artes' answer to my previous question: Subpartitioning elements of a list based on some h[ri] == h[rj] test

However, can we subpartition an unrelated list of the same length as list1, some list2 with arbitrary elements, in the same manner as list1 is subpartitioned via GatherBy?

For example, let's write some nonsense in list format:

list2 = {"It", "is", "only", "the", "morning", "the", "man", "complained", "I", "shall", "consider", "nothing"};

If we sort this list via the GatherBy output of the first list, we would have:

list2bylist1 = {{"It", "the", "man", "shall"}, {"is", "morning", "complained", "consider"}, {"only", "the", "I", "nothing"}};

Is there a way to do this simply?

Answer

list1 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}; 
list2 = {"It", "is", "only", "the", "morning", "the", "man", "complained", "I", "shall", 
         "consider", "nothing"}; 
GatherBy[Transpose[{list1, list2}], Mod[#[[1]], 3] &][[All, All, 2]]

(* {{"It", "the", "man", "shall"}, {"is", "morning", "complained",  "consider"}, 
    {"only", "the", "I", "nothing"}} *)