Potential problem re-using a SSL certificate on a newer gateway?

Figure I should ask here before I potentially cause some unexpected downtime on a production gateway as I don't know anything about SSL.

I have a 7.9 Production gateway. They want to upgrade it to 8.1. I have a new machine that I have 8.1 installed on and a backup of the 7.9 restored to.

The 7.9 had SSL enabled and presumably then had some file it used for the SSL (of what type and what location I don't know yet. All I see is something under Gateway Network Diagnostics under Local Certificate Information, a row of data with a hostname:port number, a serial number and issuer:Self).

Would it be bad to re-use that same file in the 8.1 gateway, would it cause an issue with the 7.9 or should I be asking for a new certificate from their IT team? I do not know what is proper here.

The file format used between 7.9 and 8.1 differs. I think the upgrade process may convert it, but I'm not sure you can just drop the 7.9 file into 8.1.

Certificates identify a machine by hostname or IP address. It doesn't sound like these are the same gateways, so even if you could drop the file in it wouldn't be the right certificate.

That's all I needed to know. Appreciate it.