Web hook on "Order updated": How to determine if order was converted to Invoice

I have a web hook on the "order updated" event, and I'm receiving the old and new ids without problems.

On my server I'm trying to determine whether:

1. A new order was created
2. An order was updated
3. An order was deleted
4. An order was converted to an Invoice.

I'm having trouble getting number 4 to work. The only thing I have to work on, is the old id, and I don't see any SOAP methods that can translate the old entity id to an invoice id (if the invoice exists). I've tried several hacks, but with no luck. I hope someone here can help.