If you give us an idea of the scripts you’re using for your site someone here may be better able to offer advice, or even tell you precisely what you’ll need to change if they’ve migrated similar software before.
I’d do it like this:
Setup the Fully Hosted domain so you get a folder mapped in your userspace.
Delete the newly created folder (remember the name).
Do a recursive copy of the sub’s folder into HOME.
Rename the newly copied folder to the foldername you deleted in step 2.
Keep your original sub folder in it’s original location for now, in case things don’t pan out
In the new domain folder, go through all the config.php, settings.php, etc. checking for any hardcoded paths that might be there. Check the database for similar names (config, settings) for any paths contained in there as well.
By now propagation will be complete and you can test it in your browser.
Good luck with it!
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