It is also possible to make a bootable USB stick with the High Sierra installer on it.
It is a good idea to keep a copy safe on an external drive should you ever need to reinstall macOS High Sierra (saves having to go through the painful download process or having to access the unreliable Apple Recovery Servers) or want to install it on another mac you have. When the download has completed and you have confirmed it is 5.23GBs in size then please make a copy of it for safe keeping, As I say the one in the Applications folder will self delete after you complete the installation.
And also make sure the iMac is connected to your router via cable and not WiFi. Restart your mac and go back to the App Store and try the download again, make sure the App Store says 'Get'. Ok on your iMac you have macOS High Sierra.appdownload, as you can see it is only 415kbs, move it to the Trash and empty the Trash. If you have downloaded it to your laptop and installed it the Install macOS High Sierra.app self deletes after installing, whereas you could have just made a copy prior to installing so that you could move it over to your iMac. Wish you had told me you were trying to install macOS High Sierra on two different macs.
