I run the Apache web server in a Windows enviroment for this purpose. I had to install the mod_md.so module, which, among other things, takes care of automatic exchange, thus extending of SSL certificates.
I am not going to describe here how and what needs to be done to make this things to work. I just want to describe a problem that I've encountered. That is, you will not receive any notice on the key exchange, but this is important. Just after changing the certificates, we must also restart the web server to load them into memory. If we forgot on the restart, the server could work with an already invalid certificate. Let's Encrypt certificates are issued for 3 months. However, it is arranged that the exchange takes place sometime in the third month of their validity. Although is my contact email listed everywhere, I haven't received any exchange notification yet. Therefore, I decide to monitor the automatic certificate exchange myself and of course automatically.