Deploying an Application on Apple Store

Hi, I did a Unity Mobile App project. I'm working for a University and I have my own Developper Profile, and I did the developement and the testing of the App with it.

Now it's time to publish the app on the Apple store, and the client (which is a public city departement of urbanism) want to publish the app with their Developper Profile (to be owner of the App as we decided from the begining). They just create me an account to their iTunes Connect Profile and I'm not sure I can create a distribution Certificate to put the App.

I'm a bit confused on how to deploy an App on the Apple Store with their Name associate without having fully access to their Profile. I can't either give them the full Unity Project because I don't want to give them the content of it (scripts, etc).

Thanks for your advice.

Benoit