Forum Discussion
Notification when external user accepts sharing invitation
Within the Security & Compliance center you can filter by accepted invitations. So no email alert but at least you can get to the infromation:
Can you check in Azure AD after sending the share request? I'm guessing that the AD entry isn't created until after the external user logs in but you never know, I've not tested that scenario. If they are created at share time, you should be able to add them immediately to the group.
Otherwise, you are probably faced with writing a script that queries the combined audit log (that's the one that Dean pointed out the interface for). I believe this is possible but it is still early days for that log so examples might be thin on the ground. You would then have to run that periodically and have some way of sending notifications (probably a reasonable use case for the new Flow tool).