The question is whether he is saying/ playing the parts of the actor and the mother, or whether he is the actor mimicking what the mother says - either after she says it or pre empting her as they have had similar conversations before and he knows what she might say.
I think there is one role on stage, the actor, and when he speaks the mother's words he is mimicking her. Two of the ways you suggest, after she says it or in parallel predicting what she says, are good ideas and both are valid.
There are tricks to help you playing the actor talking and the actor mimicking, for example putting the pretend phone to the other ear to suggest the other character. But after a while it is tiresome to always have the phone to the ear so it could be gradually be phased out. Other methods are of course possible.
Does this seem sensible? How do you think you will do it?
Iain