According to the CAA it is permitted. The student must be signed out by a supervising FI and must remain in the local area as it is considered consolidation flying. They are not permitted to land away as the solo cross country requirements have already been met and signed off.
I commonly sign solo students into the local area and circuit post LST having previously been of the opinion that you could not. I have the email from the CAA somewhere with the confirmation on it.
They are not allowed to self certify and the supervising FI must be on site and approved for the role in the ATO approval.