I have a server out there that supports HTTPS using a certbot/letsencrypt certificate.
I am doing a general software upgrade so to minimize risks and downtime, I'm installing new releases on a new server on which I import the live server data for tests. When everything works I'll have the DNS record changed to point to the new server.
My question is what should I do for the certificate? Can I just copy over the existing one and let it get renewed when necessary? Or will the certificate be incompatible and/or LE will complain that the address has changed during the auto-renewal process? Will LE be sensitive to reverse DNS (it may take some more delay for the reverse DNS to work). Is there any other problem I didn't think about?