Assign Rights to the Email Alerts for the User:

1.       Open the System Role

2.       Select the Feature Permissions tab

3.       Select Assign Feature Permissions

4.       Open the Configuration node one the left 

5.       Highlight the Alerts node

6.       On the right select Grant All or assign Individual rights to alerts as needed

7.       Click save

8.       Open the user

9.       Go to the Email Preferences Tab

10.   Enable Email alerts for the user

Note: To enable the Appeal Assigned Alert the user needs rights to Appeals in Fundraising Efforts as well.