Don't worry. I trade through interactive brokers. It took me...

Don't worry. I trade through interactive brokers. It took me some time, but after some persistent chasing they came through. You need to have your HIN handy. A HIN is a unique number that is issued by the Australian Securities Exchange (ASX) when you become a client of a broker. All shares that you buy through that broker will be connected to your HIN. You can find your HIN on a CHESS statement.
Don't disclose this on the phone, but they will give you a form (I suspect) to complete and send though to facilitate payment of funds. If they call you, providing your name and date of birth should suffice to allow them to find you on the share registry.
The process you went through to get a HIN will have contact details (either email or postal address) which they will reference to send forms to (make sure this is current).
Goof Luck on your investment journey.