Tried out some of the options for using VSCode LiveShare in GitHub Codespaces. You can...

1) Share from Codespaces (code window) via a link
2) Share as READ-ONLY -or- READ/WRITE
3) Share to remote VSCode browser -or- VSCode local desktop

Share FROM my Codespaces instance ->

Share TO his local VSCode instance <-

Thanks to @jeremybytes for testing this with me too.