This is a great plugin and it solves most of my problems I have with one of my websites. The only issue I am dealing with is that the images are not part of the post's Gallery because they are saved in a subfolder named /HLIC/.
Is there any way to add the images to the post's Gallery automatically?
http://wordpress.org/extend/plugins/hot-linked-image-cacher/
Try Cache Images which adds images to WordPress media library and default upload directory.
Cache Images which adds images to the media library from external sources not from a sub-folder within the media library.
I meant to try it instead of Hot Linked Image Cacher for sideloading from external sources since it will do complete job.
For adding of images to library that are already on a site, you need to create new functions (eg. based on Cache Images) or you can try W3 Total Cache which advertise feature like that (I didn't try it).