Can I share a proposal via the API?

Yes! If you would like to use the API to share a proposal rather than the UI, you can do by using a PUT request with a course, such as https://{{institution}}.kuali.co/api/cm/courses/789457894357090/sharing and including both the id of the user, and their displayName. A example of this would look like:

[{
"id": "457891313879845245",
"displayName": "Pam Beasley"
}]

You can get both of these items by looking up the user's account.