The simple answer is yes, your wife can put money into an Australian savings account as a non-resident. In practice you will need to check the different banks and their specific accounts and application proceedures to make sure that your wife can be an account holder, but it is certainly possible. However, there may be tax considerations of which you may not be fully aware. You need to consider how you (and/or your wife) will be taxed in Australia and how you will be taxed in your country of residence, whether that be New Zealand or the UK.
As far as Australian tax is concerned, regardless of your citizenship, you need to consider whether or not you are a resident of Australia for tax purposes. Having been away for 2 years already and with no apparent intention to return to Australia, you would probably be considered a non-resident for Australian tax purposes (although you should obtain advice from an Australian accountant after fully explaining your circumstances). Your wife would also be a non-resident for Australian tax purposes. As non-residents for Australian tax purposes, 10% withholding tax would be withheld from your savings account interest. (If you are a resident for Australian tax purposes, no tax would be withheld from your interest and you would be taxed on your income from all sources, both in Australia, New Zealand and potentially the UK.)
There are tax treaties between Australia and both New Zealand and the UK that are designed to prevent double taxation. If you are liable for tax in those countries, you are likely to be taxed on Australian interest income, with a credit for tax withheld or paid in Australia. Again, you should get advice from an accountant in New Zealand or the UK regarding taxation in those countries.
If you are indeed non-residents for Australian tax purposes and the interest rate in Australia is significantly higher than in your country of residence, it might be beneficial to invest in an Australian savings account, even after tax is considered. You should be aware, however, of exchange rate risk that will also affect your actual returns. This could work either for you or against you.
By Brandon Yip CFP®