You can't claim previous financial year's expenses in the current financial year. You can lodge an amendment for the years they relate to- we often do them for our clients - I don't know if you can do it on e-tax though, obviously being an accounting business we don't use it. Yes, if you have a very basic, straightforward tax return and don't have many deductions if any you will not get back any extra using an accountant - of course you can be assured that an accountant will always claim the maximum amount and know all allowable deductions relevant to you

Having said that, consider whether it will be worthwhile your time and/or money in lodging an amendment if only for minor adjustments - many of our clients mistakenly believe they can get back the entire amount or the majority of claimed expenses when in reality what happens is your taxable income is reduced by the amount of claimed expenses. (So if you're in the 15c per dollar tax paying bracket (varies on your income) max you'd get back (if you're paid too much tax that is in the annum) on $350 expense would be about $50 KWIM)

Also your DH's employer is in breach of the law - they are supposed to issue the payment summaries within 14 days of the EOFY - maybe throw that in his face if he tries to pull it again. All the best.