Anyone with write rights to a site group (it be a Cxense or Customer representative) can use the Share Site Group option to add a new or an existing user to the site group provided that they are already mapped to the Customer Object.
The recommended approach is to early on identify who at the customer that is/are to be the local administrator(s) and then give that/those person(s) both read and write access. The local write permitted users can then add new users and give them the user rights they see fit.
The green circled Update option correspond to write access and should only be given to those that are to be local administrators.
Clicking the Send Invitation button above will result in the new user receiving an e-mail that contains a link to set a new password in Insight, and will take the user to the Insight report.