No, no kind of conversion required. The only case where I could imagine that this is the case is when you are working with windows systems pr .net. There you would need to convert your key from openssl into the binary key format of microsoft (for the lack of a better name).
I mean: you now have fewer files on your webproxy and when you look into the acutal apache configuration you will notice that not even all the files in etc/univention/letsencrpy are even using by Apache.
The document that is important for you is Using your own SSL certificates. cert.pem is named the same in the example as it is named on your proxy. private.key is likely you privkey.pem and if you want to include the chain then you should probably use fullchain.pem for that.