The problem here is that the user created a custom author role but its not able to access the post type they want them to.
It seems you will need to recreate this role and assign your users to this role.
What I would recommend that you do is to create a new role and then allow the role to copy the permissions of your Default author role.
Once you have done this then you can delete the previous role and it should allow you to select the new role to assign your users to.
This is the technical support forum for Toolset - a suite of plugins for developing WordPress sites without writing PHP.
Everyone can read this forum, but only Toolset clients can post in it. Toolset support works 6 days per week, 19 hours per day.