This plugin allow you to grab image from remote url and save into your own wordpress media library. By doing so, you never worried if the remote image was removed by its owner. This also save you steps to download the image to local computer and upload again to your own wordpress.
After grabbing the image, wordpress will prompt you either to “insert into post” or “change attributes” just like after you upload an image. Renaming is available.

Grab & Save

This plugin allow you to grab and save the image from remote url into your own wordpress media library.

basteln3rk

This plug-in replaces the built-in “Import from URL” media upload tab to allow you to download an image from a remote URL into the WordPress media gallery. Thumbnails for the remote image are created locally, and after upload you are able to add custom media attributes (like caption, title) and insert the image into your blog post.
How to Find the Plugin:
<ul>
<li>When editing a post, click “Add Media”</li>
<li>Then select “Save & Import from URL”: If your window is large, this is in the sidebar on the left. If your window is small, you need to select the drop down menu where “Insert Media” is preselected.</li>
</ul>
List of Features:
<ul>
<li>Directly include a remote image into a blog post without having to save it to your computer locally</li>
<li>Be a better internet citizen: avoid hotlinking images with ease!</li>
<li>Rename image after download</li>
<li>Full integration with media library – including creation of thumbnail images</li>
</ul>
<h3>Credits</h3>
<ul>
<li>Builds on the idea of the <a href="https://wordpress.org/plugins/save-grab/" rel="ugc">Grab & Save</a> plugin, but compatible with WordPress 4.2+ and support for thumbnails</li>
<li>Free plugin brought to you by <a href="https://www.flexponsive.net" rel="nofollow ugc">flexponsive</a></li>
</ul>

Save & Import Image from URL

Perfect Working with WordPress 4.9.7

The tabs in the media uploader on the left no longer exist, and this no longer ends up making changes to add any new features unfortunately.

No longer works with updates that have been made since this was published.

Allows you save an image from a remote URL to the WordPress media gallery, create local thumbnails and rename image.

Grab & Save vs Save & Import Image from URL