I don't practice in NSW, but yes - I'm pretty sure.
Appointment of proxies must be done in the form prescribed by the regulations (per s26, Schedule 1 of the Strata Schemes Management Act 2015). The prescribed form requires signature by the owner and a nomination of the person appointed as proxy. It does allow for an alternate proxy if the first choice already holds the maximum number of proxies - this isn't a transfer, it's an alternate appointment.
The proxy could not appoint someone else, as the appointment of any proxy must be on the prescribed form and signed by the owner of the lot to which the vote attaches. Therefore, the proxy could not sign a valid appointment form as they are not the relevant owner.