Thanks for your response!
It is something which I will be able to implement. I have created a test subfolder in which I moved one query and one tasklist item.
What I found remarkable was the tasklist path - inside the schedule linked to it - got automatically updated as I dragged the tasklist from one folder to another.
If this schedule / task / query works fine, without errors or warning messages, I will deploy it to all my other 200 items in the shared folder in about a week's time.
Will keep you posted.
Thanks again!
Chaitali