Force Mac Installer to Continue Download
No - the installer for the reinstall uses apple's Content Delivery Network (CDN) to download the install image file in parts. There are usually about 500 chunks that get downloaded and then fused into the installer.

(I suppose someone could reverse engineer this process, but it's not documented and signed cryptographically to prevent man in the middle tampering with the downloads - so that might be costly).

What you can do is run a local caching server (on High Sierra - turn on content caching on the Sharing preference pane and on Sierra and lower - install server.app and turn on content caching).

That way whenever any device on your local network downloads these 500 items - they get cached locally and your next download only needs to get pieces that are not already cached. The first time you do recovery for the image needed - you of course download all bits from outside your local network, but until the image changes - you are set.

If you can't afford another download or set up caching server - you can go to the Mac App Store on another Mac and download the OS installer and then create a bootable USB installer - now you have no download and something bootable for the Mac you hoped to use Internet Recovery on.