list = [["f1", "object1"],["f1", "object2"],["f2", "object3"],["f2", "object4"],]

ll = []
for g in groupby( sorted(list,key=lambda x:x[1]) ,key=lambda x:x[1]):
    ll.append(g[0])

    for i in g[1]:
        ll.append(i[0])

list3 = ["f1", "object1", "object2", "f2", "object3", "object4"]

listGroup = [["f1", ["object1", "object2"]], ["f2", ["object3", "object4"]]]

items = [["f1", "object1"], ["f1", "object2"], ["f2", "object3"], ["f2", "object4"]]

from collections import OrderedDict
key_by_item_list = OrderedDict()

for key, value in items:
    if key not in key_by_item_list:
        key_by_item_list[key] = []

    key_by_item_list[key].append(value)

print(key_by_item_list)  # OrderedDict([('f1', ['object1', 'object2']), ('f2', ['object3', 'object4'])])

new_items = []

for key, item_list in key_by_item_list.items():
    new_items.append([key, item_list])

print(new_items)  # [['f1', ['object1', 'object2']], ['f2', ['object3', 'object4']]]