Hi, I’m Adriana and I’m an engineer at Trello.
I want to make sure I’m understanding you correctly. You want the API to return the link to share the board? May I ask to what end are you using this link?
Otherwise, if you are just using the link to add people to the board, you might consider using the API to add a user via email. Or, if the user is already a Trello user, you can also add a user via their member id.