That's what I was asking. How do do that
Manually using Carbon Copy cloning, with CCC you can point the source at the source and on the right the disk to be "synced" as the target, on the left you should uncheck almost all boxes except the Users box, it will sync the Home folder.
For applications you can manually copy them over, reason not to use CCC is that it will overwrite the existing Applications which are incompatible with the former OS, you could use CCC for that but then you have to uncheck each and every Application which is already on the target which is more work.
There are most likely some settings and files in the main library, normally not that many, it's a chore to know which files, you can just leave it that way, or you can use CCC to sync this one too, most likely this will not give you headaches, there's not much which can damage the former OS install, just check that box in CCC too.
Leave all the rest of the folders unchecked, those are all system files.
If it's not clear ask me and I will post a screenshot.
Edit: One thing to be aware of is the username and password must be the same if you don't sync both Home and Library, there are keychains in both /Home/Users/Library and /Library.