I don't know of a plugin!
Wordpress stores uploaded images in a media library which puts them in the posts table.
As you have copied and pasted they are not in the media library, but just as img tags in the posts/pages themselves.
Step 1 - copy the image files themselves, using an FTP to download them all then put them in newdomainname.com/wp-content/uploads/2015/04 - ie this months upload folder!
Step 2 You can log into PHPMyAdmin to quickly update all the images in the posts/pages. Change the urls ;-)
UPDATE wp_posts SET post_content = REPLACE (post_content, 'src="http://www.oldsiteurl.com', 'src="http://yourcdn.newsiteurl.com');
UPDATE wp_posts SET guid = REPLACE (guid, 'http://www.oldsiteurl.com', 'http://yourcdn.newsiteurl.com') WHERE post_type = 'attachment';
That won't have put the images in the media library for making thumbnails, feature images etc, but it will have moved them over.
You can then use https://wordpress.org/plugins/add-from-server/ to add the uploaded images into the library.