Hi Movinghouse123!
Welcome to the AGL Community!
Your mum will need to select a new plan when she organises the connection at the new property, she can do this directly on her AGL My Account by selecting the Move Home option.
We've moved away from conditional discounts such as "Pay on Time" and "Direct Debit" discounts, we're now offering low rate energy plans where the rates are already discounted for you, more information can be found on our website here.
Kind regards,
-Nam-