Yes, devices can be moved between folders. You can do this per device from the device's manage page, or you can do it in bulk from the folder list view (bulk actions show up when you click the pencil on the top right of the list table).
Please give more details about how data lost is observed. When moving a device, the historicals for that device should be intact. Group graphs should also continue to work the same since only Folder was changed. The folder level is the only area you might see, because the folder RRDs aren't unique per device, it's unique per folder. So moving devices out of the folder - the old folder retains the data to the point of the change. Then the new folder data starts to populate.