Sometimes AD synchronization stales between domain controller and SharePoint server.
This are the steps to solve this issue
1. Go to SharePoint central administration
2. Select manage service applications
3. Manage user profile
4. Find user profile
5. Edit user profile work email field
6. Go to Job definitions on Check Job Status
7. Select Job Definitions
8. Scroll down and select User Profile Service Application – User Profile to SharePoint Full Synchronization
9. Wait for the job to finish running and check if you can set Alerts for that specific user.