I don't believe this is possible with Construct by itself. You would need a backend service or other online data storage solution, at least enough to authenticate and keep track of each user.
Generally speaking, every user, upon creating an account, will have a code or link associated with their account in your database. This code/link will be available to the user to share. When a new user enters the code/link in their client, your server will be able to look up the origin account associated with that particular code/link and credit it accordingly.