There seams to be a problem in the app Store when trying to download macOS 10.14. I get the Note: „This copy of the Install macOS Mojave application is damaged, and can‘t be used ...

When you go to the App Store Mojave download page does it say Open,

it should say Get or Download.

If you see Open then the App Store has detected a copy of Install macOS Mojave .app in the Applications folder.

Locate it, move it to the Trash, empty the Trash.

Connect your mac to your router via cable.

Restart your mac go to the App Store Mojave download page,

do not use the mac while it is downloading or any other devices that share the same internet connection.

AFAIK the Mojave installer has not been updated since fall 2019 so it seems unlikely that it is corrupted at Apple's end (is it the about 6 GB full installer, not a tiny stub installer that has sometimes plagued folks trying to make a bootable USB flash installer?). So try again. Or does booting in safe mode help? Or creating a USB flash drive installer from the download and option-booting from it? Is the Mac's system clock on time (the similar problem with some old installers with old certificates could be fixed by turning the clock backwards while off-line)?

The usual answer to this question is to trash the old Installer from /Applications, reboot, then download a new Installer.

The installer from the App store is not damaged, something has gone wrong with your

copy. Delete it, follow my instructions and download it again.