SYMPTOM:
When a Web user subscribes to a report or document to be added to History List with delivery notification option selected, some users receive an email with "Link to history list," while the other users do not see it for the same subscription executed at the same time. Following example indicates that Administrator user received a notification with the link while AUser's notification does not.
Delivery notification sent to Administrator:

Delivery notification sent to AUser:

AUser is able to see the report in History List without any issue. The link was available only in the email for Administrator.
CAUSE:
This behavior is caused by the fact that the AUser does not have the privilege "Use link to history list in email" listed under Deliveries as shown on the image below:

ACTION:
Ensure that all users who need to receive the link to the History List message in the delivery notification have been granted the Use link to history list in email privilege.