Here's one approach:
sublists = {{1,1,1},{2,2},{3,3,3,3}} list = {4,5,6} Map[Flatten,Transpose@{sublists,list},{-3}] (* inline-edit: please, please, don't use this *) (* {{1,1,1,4},{2,2,5},{3,3,3,3,6}} *)
Not too great, especially if the elements are non-atomic expressions.
Map[Flatten,Transpose@{sublists,list},{1}]
or
Flatten/@(Transpose@{sublists,list})
seems a safer solution.
Or with Append:
Append@(Evaluate@(Sequence@@#))&/@Transpose@{sublists,list}
I'm still wondering, how to get rid of that Transpose without a loss of the functional approach.
EDIT of course, silly me, I've overlooked MapThread as provided in the linked question.
MapThread[Append,{sublists,list}]
EDIT2 some benchmarking.
sublists = RandomReal[5, {10*^5,5}]; list = RandomInteger[5,10*^5]; First@Timing@MapThread[Append,{sublists,list}] (* 1.154407 *) First@(Timing@(Append@(Evaluate@(Sequence@@#))&/@Transpose@{sublists,list})) (* 3.057620 *) First@Timing@(Flatten/@Transpose@{sublists,list}) (* 2.012413 *)
Obviously MapThread (as also provided now in the comments) is the way to go.
More options
As in my first two approaches Flatten performed better than Append, I figured, there must be a better way.
First@Timing@MapThread[Flatten[{##}]&, {sublists,list}] (* 2.589617 *)
(deleted approach with Join, as it was incorrect, corrected version doesn't improve speed, will look for other fast methods)
MapThread[Append, {{{1, 1, 1}, {2, 2}, {3, 3, 3, 3}}, {4, 5, 6}}]$\endgroup$