Ask HN: Utilities / Techniques for transferring installed applications

A relative of mine just bought a new laptop to replace their previous one (that is now heavily damaged, but barely usable). They have Microsoft Office and Intuit Quickbooks (among other things) but have long since lost the installation media. They asked if I could help them transfer the software to the new computer. Despite all the system recoveries I've done, I've never actually transferred complete applications from one machine to another. I'm betting it's a lot more involved than copying directories, as there must be countless registry settings that can't be copied directly.

Are there any recommendations on how to go about doing this? I have a couple of weeks to get it done and I don't mind buying a fairly inexpensive tool if I can get it quickly. I read about Move Me, but I'm wandering if there's a better (or DIY) alternative.