Whenever a notification email is sent to your customers, the FROM address that is used can be changed by doing the following:
1. From the Back in Stock - Restock Alerts.
2. Go to Customize-> Email Template
3. On Email Settings, go to From Email Address
4. Once the, update it your new email address
Note: Using Yahoo or Hotmail email addresses may cause issues with email delivery. Use your company domain email address. Also, make sure to double-check the new ‘From’ email avoiding any typos to ensure email delivery.