Currently if a Program is set as Invite only, you open the Contact record and use the Invite button. The last step of that process is to select an organisation name. Unfortunately the list is blank if the Contact's Organisation is not one that is listed in the Blackbaud Verified Network (BVN - formerly NPO Connect).
This severly limits the use of the Invite functionality.
The ideal would be to pick up the organisation name from the organisation record associated with the contact - and have a pick list if they are associated with many organisations.