Have a look at the pointer from Mike_James - however, I have developed an app for a client that has now taken over backorders in their MYOB system - and invoices get added and deleted all the time especially SOrders.
And I also delete them from my app.
Each invoice has a URI - as does each SO - however, in my initial build of my app I struck this problem and built a copy in my app of all invoices in myob - and cross checked this everytime I updated - and produced an error code if an invoice had vanished - I think this is your simplest way - invoice id are not unique enough but uri are and are only accessible via the API.
My system works ( actually if I get a duplication of an invoice/SO number it causes a problem but that is by design - not as a fault) - but for the MYOB API to delete an invoice or SO it is very easy - it just needs the uri - which for duplicate invoice numbers or SOs are unique.
Hope this helps but it is a relatively easy solution to code.
The Doc
