When using the CloudBees Folder Plugin it is possible to move a job/item from a folder to another. Currently such operation looses the history of config changes in the job because the job config history files aren't updated/moved

For this you probably need to implement the standard relocation handler to update job config history files accordingly: https://github.com/jenkinsci/cloudbees-folder-plugin/blob/master/src/main/java/com/cloudbees/hudson/plugins/folder/relocate/StandardHandler.java