LogFAQs > #986329490

You can turn the money in more or less whenever, that's just step one in the process. You've got another questline to get through before you're actually ready to go. I recommend doing it, though, the guy you'll be sent to talk to gives you several great items, including an amulet that'll be useful on someone for basically the rest of both games.

I'm usually cheating my ass off so I get the quest and turn it in on the spot, get back-to-back "new chapter" videos.