From the rules : Any sea zone that contains only enemy sub. does not stop the movement of a sea unit. … . There is an exception … A submarine can attack any transport that moves into or through its sea zone unaccompanied by surface warship (note : submarines are NOT surface warship) … Each submarine fire once (att. 2) at the transports … any undestroyed transports can continue their planned movement.
Note : sea unit ending their combat movement in a zone containing only enemy sub may choose to attack or not.
But that doesn’t answer whether you can engage the sub with your sub AND move the transport through, which I felt was the gist of the question. I don’t believe you can. Once a seazone is contested, all movement should be blocked. So you can choose to ignore the anzac sub (and he gets a free shot), or you can choose to engage the anzac sub (and the subs fire on each other), but you can’t choose to do both. Unless you can. Which I guess is ok, but still wierd. In which case the Anzac sub should still get a pot shot.