You can do one thing, use this plugin, this will help you in exporting all featured images either it’s of any post type. Follow these steps:
- Export all images from the existing website and import it in the new one.
- After the images have been imported successfully, now continue with the importing of posts/post types.
Importing Images first will get all the images of that post type, and when you will import posts these images will be assigned to respective posts.