How do add a the style-mobile css from the main theme to the child theme?

It is mostly matter of personal preference how to structure this.

The typical approaches are:

  • CSS import (used to be popular, but considered kind of meh now);
  • enqueue parent stylesheet as dependency and customize with rules in your stylesheet (more files, less trouble);
  • copy parent stylesheet into child completely either once or repeatedly via build tools (less files, more trouble).

If you go with enqueue you can retrieve URL to parent theme with get_template_directory_uri() function.