We usually run into this issue while migrating site from one domain to another or during migration from wordpress.com to wordpress.org
There are couple of plugins which you use to import external images. One of the popular one is https://wordpress.org/plugins/auto-upload-images/ However this plugin didn’t worked for me. I tried this plugin https://github.com/VR51/Import-External-Images-2 from github which downloaded all the external images.
If there large size images then above plugins may not work properly, sometimes due to hosting restrictions. Try to identify the post where it the process halts and then do that manually.