For a site without any particular framework, simply copy the site files directly to the new directory for the Add-on domain.
If you are trying to move a WordPress site, though, things get a bit more complicated. I'd suggest just using softaculous to clone the WordPress site to the new domain, as this will save you the trouble of having to move/rename the files in file manager, reconfiguring the home and site url, and other details.
Lastly, if this is your primary domain you are changing, please follow these steps to change the primary domain: but keep in mind that the two things are separate and it's easier to sort out the site before switching the primary domain.
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