Install from a backup?

Hi, a WP website I made for a friend became corrupted or hacked. His hosting company were incredibly unsupportive and the result is that now I am unable to log into the site. The hosting is due soon expire soon and he will be definitely changing to a better hosting service!

Fortunately I have an UpdraftPlus backup in Google Drive on my computer. Is there a way I can use this to restore the website when he starts the new hosting account?

I will be installing Updraft Plus. Can I make it connect to the backup files and use them to restore the site? Do I need to manually upload them? Do I need use the migrate function?

Obviously I’m new to this, so any advice would be appreciated!