I was not really accessing this directory publicly by url as the example you asked, but before seeing your answer I turned on the old machine that already had the keys generated for my certificate and copied the /etc/letsencrypt directory to my new machine .
Then I took the step of editing http.conf, adding the path of these keys:
Copying the /etc/letsencrypt directory is fine, but if there’s any doubt remaining about the renewal process, it will still be good to figure out what’s going on with the challenges because your most recent certificate for that domain will expire on October 24. So you will eventually need to be able to pass challenges from the CA to get a renewed certificate…