Functionality to migrate customization ap1 entries

I love the customization panel that has been added to themes. It makes things a lot easier. However there is one problem – when migrating a site, the customization is lost. The fact that I might have to reenter all that data is an inconvenience, which would be nice not to have, but at least you have your original development site to copy the data from.

But recently I had a situation that demonstrated to me the actual need to migrate customization data. Tech support of my hosting provider damaged my development copy of wordpress, such that I could not login and access my customization data.

This may be already available information in the migration package or database, but the location of the theme customization is not publicized to the user – as far as I know (please inform me if I am wrong) nor how to automatically populate the customizer fields from the data if it exists.

It would be really helpful, if the information is currently available in migration data, it were publicized and instructions given for accessing the data. If I’m right, and the data is currently not available, creating such a vehicle – especially making it an automatic part of a migration – would be really helpful.