I don't understand why this question was closed on the grounds of "that this is an opinion poll", that I am asking what is the right approach in a given project management situation: https://pm.stackexchange.com/questions/33461/who-should-be-responsible-for-preparing-a-tasks-written-assignment-between-an-a.

My questions clearly requires a definitive response, not an opinion. Moreover, what a professional considers a right approach in a given situation is not a matter of subjective tastes or moods, but straightforward solution which can only be described by specific arguments and logic.

Not to mention that this statement in the comments "It is also not scoped to project management; you are seeking opinions and discussions about a wider principle of responsibility" is completely untrue and shows that the author has not even taken the effort to understand the question. The question has nothing to do with "a wider principle of responsibility". It is about efficient allocation of roles in a project management process.