Custom Post Type not visible by user

Hello

I’m using a custom post type and would like to give a user access to one specific post type. However, the user doesn’t get access to the existing one, but can only create new ones. He can see that there are two posts, but only the one created on his own is accessible?!

Below you’ll find the custom post type and the permissions I set.

Does anyone know what I’m doing wrong? Before buying this plugin, I have to make sure it works the way I want it to. 🙂

Thanks in advance for your help!