Obviously two wrongs, both egregious, don't make a right.
There are ethical, contractual, and criminal issues involved.
If an apparent agent of the employer promised to reimburse the expenses by company policy or directive and in doing so led the employee to incur necessary and reasonable business related expenses that they otherwise would not have incurred, then the company is guilty of poor ethics, breach of promise, and is in effect stealing from the employee by refusing to pay.
However, if the employee willfully and maliciously acted in such a way that they caused provable $ damages to the company, then the company should so claim and offer to settle accordingly $ for $ with the former employee.
Threatening to report the employee, only if the employee persists in their claim for expense reimbursement appears to be extortion by the employer and underscores the probability or at least the possibility that the employee caused no actual damages to their employer. Expense reimbursement is a separate issue from the bogus invoice issue.
The employee said they eventually voided the bogus invoices. That potentially means two things that could be to their credit: (1) they stopped or reversed the damage and the theft before conclusion; (2) they may have done so out of remorse rather than, for example, a fear of getting caught or having gotten caught.
While there is obviously additional relevant information that is missing, based on the information given, the employer had the right to terminate the employee for employee fiduciary failure reasons. The employee has the right to be reimbursed for their reasonable and necessary business expenses and the employer has a fiduciary duty to pay those expenses.
NOTE: I am not an attorney.