Here is my research on available plugins that are able to cache external images locally, and do that automatically; so called, sideload external images or local image caching.
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In the following articles, here and here a lot of old plugins have been listed.
But the only ones from that list that are still maintained are:
By digging deeper into Wordpress.org’s plugins repository, I found more plugins that are still actively maintained:
This plugins is not for that exact purpose, but a helper when editing to import image from some external site:
Sideload images
WordPress: Import Images From Another Website - HtmlCenter Blog
http://www.htmlcenter.com/blog/please-stop-using-curl-in-wordpress-plugins/
This plugin localy caches images also, so steal from it: Content Cards Content Card images are now cached in Media Library.