MacBook Pro won't install Mojave

The InstallOS.dmg contains the installer for macOS Sierra, so why you are downloading that I don't know.

If you want to install macOS Mojave, click on the link below.

Open your Safari browser, Firefox will not work.

How to upgrade to macOS Mojave - Apple Support

Go to Section 1 and confirm your mac can upgrade to Mojave,

if it can go to Section 4 and click on Get macOS Mojave.

This will redirect you to the App Store and the Mojave download page.

It should say Get or Download.

If you see 'Open' this means the App Store has detected a copy

or partial copy of the Install macOS Mojave.app in your Applications

folder, if that is the case that is why you get the error,

"This copy of the Install MacOS Mojave application is damaged......."

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

Connect your mac to your router using a cabled connection.

Restart your mac, try again.

Do not use the mac while it is downloading.

If there are other devices that share the same internet connection

don't use them either while the mac is downloading.