I am trying to update from macOS 12 Sierra to macOS 13 High Sierra, but on the Apple App Store I am getting this message: This copy of the install macOS High Sierra.app application is damaged, and can't be used to install macOS. What can I do?

Delete "Install macOS High Sierra" from the Applications folder then re-download while in Safe Mode.

How to use safe mode on your Mac - Apple Support

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...

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, empty trash & restart, then a new copy of a more recent version can be downloaded…

Thank you for timely reply, you gave me hope that I have not lost my system. But pls can you guide me on step by step way of deleting "install macOS High Sierra" from the applications and on how to re-download it into safe mode.

Thanks a lot for your kindness.

welcome.

Great to hear, dialabrain is a great helper. :)