CPTs don't show up at all users?

I have registered a custom post type and would like to add entries of this CPT into my menu. I have multiple users with the Admin Role, but they only show up under one specific user – the others simply don’t see the Custom Post Types.

// functions.php
    function register_cpt_trainings() {

        $labels = array(
            'name'                => _x( 'Trainings', 'Post Type General Name', 'somedomain' ),
            'singular_name'       => _x( 'Training', 'Post Type Singular Name', 'somedomain' ),
            'menu_name'           => __( 'Trainings', 'somedomain' ),
            'parent_item_colon'   => __( 'Eltern Training:', 'somedomain' ),
            'all_items'           => __( 'Alle Trainings', 'somedomain' ),
            'view_item'           => __( 'Training anzeigen', 'somedomain' ),
            'add_new_item'        => __( 'Training hinzufügen', 'somedomain' ),
            'add_new'             => __( 'hinzufügen', 'somedomain' ),
            'edit_item'           => __( 'Training bearbeiten', 'somedomain' ),
            'update_item'         => __( 'Training aktualisieren', 'somedomain' ),
            'search_items'        => __( 'Durchsuche Trainings', 'somedomain' ),
            'not_found'           => __( 'Nicht gefunden', 'somedomain' ),
            'not_found_in_trash'  => __( 'Nicht im Papierkorb gefunden', 'somedomain' ),
        );
        $args = array(
            'label'               => __( 'trainings', 'somedomain' ),
            'description'         => __( 'Trainings', 'somedomain' ),
            'labels'              => $labels,
            'supports'            => array( 'title', 'editor', ),
            'taxonomies'          => array( 'category' ),
            'hierarchical'        => false,
            'public'              => true,
            'show_ui'             => true,
            'show_in_menu'        => true,
            'show_in_nav_menus'   => true,
            'show_in_admin_bar'   => true,
            'menu_position'       => 5,
            'can_export'          => true,
            'has_archive'         => false,
            'exclude_from_search' => false,
            'publicly_queryable'  => true,
            'capability_type'     => 'page'
        );
        register_post_type( 'trainings', $args );
    }

Unter Design / Menu, I expect them to show up on all admin users, but the other ones only have the default entries “posts”, “page”, “links” and “categories”.

My user also has the “training”.

Any ideas?