Well the simple answer is that it's time travel... so even if it took years for the observers in the future to rebuild, once their operation is back in order, they can still send stuff back to that specific time. At least that's what immediately came to mind when I watched it.
That's what I assumed, too, until I took a moment and thought about it. I mean, the whole point of the final piece of the box was that if he put it in wrong, both he and the Observer would be turned to ash. Not that there were two possible means of accomplishing it without the device exploding, but only one out of four.
Then, after Peter returns, the Observer was acting like he pulled off some amazing dupe on Peter, and that by putting that last piece in the way he did, he somehow sabotaged his efforts. Even though, again, we saw that the box worked and that it did, in fact, connect with the/a future where they were sending back the cargo.
So... yeah. I'm just completely lost about what any of that was supposed to mean.