There are problably a million blog posts telling you how to do it, but none of those guides worked for me. Things can often be different sites and other "unknowns", so there is no guarantee this works for you or for every site.
First we'll use curl to search for all the relevant files for the domain and based on the snapshot/timestamp in bold below.
curl -s "https://web.archive.org/cdx/search/cdx?url=yourdomain.com/*&to=2........
There are a few ways of doing this and all basically involve using the reverse proxy or "ProxyPass" feature of Apache to accomplish it.
1.) Create a normal vhost and simply symlink the root directory of the site you want to mirror.
Eg. originalsite.com and newsite.com
/vhosts/originalsite.com/httpdocs
You would symlink like this:
ln -s /vhosts/originalsite.com/httpdocs vhosts/originalsite.com/........
This is something that happens a lot and it is very dirty, as you probably know each site is hosted on a certain IP address. Sometimes a domain is hosted by a single IP address and the IP address defaults to this very same domain.
This means that if someone buys domain abcd.com and enters your IP address (the one of your website) as the A record, your content will show up on their domain as if it was their own.
There is an easy way to prevent this by using .htacces........