After visiting McGonagall and receiving her message, Harry dispatches his own patronus to pass a message to the warehouse.
But in this case, his patronus will still have to show up at the warehouse. IOW, it doesn't alter the prediction that a patronus will show up at the warehouse to give them the message.
From there the message passes to Mary's room, and from there to Flitwick as an errand run on the on the way to Azkaban.
They already went to Azkaban, so they can't undo that to run an errand. The message would have to be sent on their return trip from the warehouse, i.e., before Harry's "rescue" from the washroom. These are the only currently-blind spots in the story where a change can occur now.
What's still not clear to me is whether this is even remotely possible within the story's current timeline. Aside from it being not at all clear what the current clock time is throughout the story, the mere fact that the time turner was used in an overlapped way (first turning back to before lunch, then again back to the same point after the prison break), may mean that their total travel may not span the full six hours.
They already went to Azkaban, so they can't undo that to run an errand.
I'm guessing that Eliezer forgot to tells us about the errand in the earlier narrative.
- This thread has run its course. You will find newer threads in the discussion section.
Another discussion thread - the fourth - has reached the (arbitrary?) 500 comments threshold, so it's time for a new thread for Eliezer Yudkowsky's widely-praised Harry Potter fanfic.
Most of the paratext and fan-made resources are listed on Mr. LessWrong's author page. There is also AdeleneDawner's collection of most of the previously-published Author's Notes.
Older threads: one, two, three, four. By tag.
Newer threads are in the Discussion section, starting from Part 6.
Spoiler policy as suggested by Unnamed and approved by Eliezer, me, and at least three other upmodders:
It would also be quite sensible and welcome to continue the practice of declaring at the top of your post which chapters you are about to discuss, especially for newly-published ones, so that people who haven't yet seen them can stop reading in time.