Not possible. Soholaunch is a web-application (script), and not a system of files.
You will have to create an entire backup of your "site," create a new add-on with the domain you want, install Soholaunch fresh to that add-on, and then "skin" the new installation with the backup of your old.

* Remember to edit the configuration (the domain names) prior to backup, otherwise a fatal conflict will occur.

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