When I checked the edit screen for the "МИУs Онлайн" post type that you shared, I noticed that only the users with the "Administrator" role were showing in the post author field.
That is because in the settings at WP Admin -> Toolset -> Access Control -> Post Types, under the post type "МИУs Онлайн", only the "Administrator" and "Editor" roles had the "Publish" permission.
( screenshot: hidden link )
As an example, I've enabled the "Publish" permission for the "Teacher" user role too and the users with this role are now also included in the post author field for this post type. Similarly, you can also add publish permission to other user roles too, to include them in the post author field.
I hope this helps and please let me know if you need any further assistance around this.