Unfortunately, if the owner of the content is not interested in keeping this site up, the content will be lost sooner or later anyways. He probably also does not bother to install security updates and he will most likely stop paying the bills at some point (domain name, hosting server, etc).
Installing LetsEncrypt is not much work and he might be motivated if a lot of people ask him. If he is really not interested, it is probably best to archive the website to a real archive and hope they make sure they content remains available. Unfortunately this also means that the archive will no longer be found on google or most other search engines. It is really a shame that there is no work on google's side to make sure archived content can be found among other search results.
> Installing LetsEncrypt is not much work and he might be motivated if a lot of people ask him.
Assuming he has direct access to his server of course. If he's on a shared host, he may not have the option to use LetsEncrypt, but may be forced to a buy a certificate from the hosting company.
Many hosting companies already give out free LetsEncrypt certificates with the ease of a checkbox. And those that don't will have plenty initiative to do so because their customers will spam their support saying that their website is not save anymore (and many will switch if the price for the certificate is unreasonable).
Installing LetsEncrypt is not much work and he might be motivated if a lot of people ask him. If he is really not interested, it is probably best to archive the website to a real archive and hope they make sure they content remains available. Unfortunately this also means that the archive will no longer be found on google or most other search engines. It is really a shame that there is no work on google's side to make sure archived content can be found among other search results.