High Sierra download has a damage message, what can I do?

Remove that High Sierra download, and use the Safari browser to get High Sierra again from How to download macOS - Apple Support provided your download is not to a Mac that originally shipped with a later operating system.

VikingOSX has you covered, but if short of Data or Bandwidth...

If you get a corrupted message...

Naw, not damaged, it's just that you have an old copy already in Applications, there are 2 cures...

If you’re short of bandwidth or data…Disconnect from the Internet & set the Date back to 2014, then you can run the Install MacsOS High Sierra App in Applications, so expired Certificates are not expired.

Or... trash the Install MacsOS High Sierra.app in Applications then Restart & a new copy more recent version can be downloaded.