To send an e-mail to an employee once the expense report filed has been approved by supervisor/expense approver/accounting.
Perform the following steps:
Navigate to Setup > Company > General Preferences
Put a check on the box on the EMAIL EMPLOYEE ON APPROVALS field
For an email alert to fire once accounting approves Expense Reports, the Approve button should be used instead of the Accounting Approval check box.
Please refer to Answer ID: 8516 Giving Accounting Approval for Expense Report, for the steps on how accounting should approve Expense Reports.