How to let a customer translate his Kirby website?

No, the language setup has to be defined in the config.php file.

Edit: see also my suggestion here: Translation and config.php Bug?

It is important to keep in mind, though, that if a user deletes a language from the configuration, the then unnecessary text files for that language would have to be removed manually from the file system (unless you write a plugin that does that as well), because otherwise these files could cause trouble in the Panel.

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