Invited admin isn't receiving emails

Presumably other people are able to receive emails sent from this website.

Is it possible that the website shares hosting with another site which has been put on a spamming blacklist ? Maybe your new admin’s email service is blacklisting your email on this basis.
Does your new admin have another email address ? Try it.

I understand that when your new admin tries to view the admin login page, that he gets a white screen. Can he view your website’s regular homepage and other pages ?

Can you get your new admin to use a different browser ? A different computer ? A different internet connection ?