Export settings to child theme

Hello what would be the best way to export the theme settings to a child theme?

Use case:
Site owner has created his website with this theme and has customized to his liking. Then he wanted more functionality and has hired a developer (me). Now I need to create a child theme, but when I activate the child theme all the settings are not transferred to the child theme.

What is your recommended procedure to transfer all theme settings and customizations to the child theme?