Thank you for your reply.
All the permalinks will stay the same as all URLs should stay the same. There should be no changes on the front-end. zzz.com will stay zzz.com and yyy.com will stay yyy.com. The only difference is that instead of zzz.com being the primary, now it’s yyy.com (and therefore, the redirect that the server does behind the scenes is different).
From that page it reads:
“Keeping Your Domain Name and URLs
Moving your domain without changing the Home and Site URLs of your WordPress site is very simple, and in most cases can be done by moving the files.
If database and URL remain the same, you can move by just copying your files and database”
How do I know if the database remains the same?