At the very least, it sounds like your organization needs to look at this person's duties related to finance. The person handling the banking needs such as making the deposits and reconciling the bank account should not also be handling the recording of incoming receipts or outgoing payments. This seperation of duties is a key concept of internal controls and helps to prevent fraudulent activity by one person. The one drawback is that it requires additional employees to split those duties which should not be shared by one person.There is plenty of information available about separation of duties on internet.

As an accountant, I see a huge red flag thrown up by the dishonest actions and a closer eye should be kept on this employee until an adequate separation of duties can be achieved.

Personal policies should be used to handle the firing issue and they may specify that a reprimand is required for the for the first offense. Considering the offense, I personally believe immediate firing would have been justified. But I'm not an attorney-just an honest accountant.