NONE of the copies of Mojave that you have downloaded are actually damaged. The message that you are receiving is due to them having what is known as an "expired certificate." A "certificate" is a security measure that Apple uses, which they need to periodically renew.
Every 10 years ALL installer certificates expire no matter how old an individual installer program is.
Redownload Archived macOS Installers to Address Expired Certificates - TidBITS
When you have an installer for the Mac OS with an expired certificate, you can re-download the installer for the old OS to get one with an updated certificate, or you can set the date on your Mac back to fool the certificate into believing that it is still within the date of its certificate. However, both of these methods aren't 100% sure to work.
The method that does seem to consistently work is to simply neuter the resource in the installer program that keeps track of the freshness date. It's easy to do:
1. Go into the Applications folder.
2. Find the Installer for macOS in your Applications folder
3. Right-click (or Control-click) on the installer and choose “Show Package Contents”.
4. Open the folder named “Contents”.
5. Open the folder named “SharedSupport”.
6. Delete the file named “InstallInfo.plist”.
7. Enter your administer password to confirm.
8. Now the installer for MacOS will work perfectly.
If you don't still have the copy(s) of Mojave that you previously downloaded, you can download another copy from:
macappstores://apps.apple.com/app/macos-mojave/id1398502828?mt=12