No.
Take it back to reproduction. The root of male and female and the reason the descriptors exist is reproduction.
Undeniable (intersex people are male or female, nor a third sex)
Ask him to what these descriptors apply, if not human reproductive role.
Point out that the descriptors male and female can apply only to gender identity OR the reproductive role, as the two can be in direct opposition.
So for example, he believes gender identity overrides the reproductive role, so the XY person is female, therefore cannot have a male body, the body must be female
(at this point he may say it's a female brain and a male body, in which case you say, what are the objective criteria for a female brain, and what does female mean if it isn't attached to reproductive role, and also note down that he accepts the body is male, for use later on in your thrashing good argument)
So if male and female are completely detached from reproductive role as required by faith in gender identity then there is no 'male' or 'female' meaning for the gender identity to be ascribed to.
At this point he will be forced to describe the female brain in terms gender stereotypes and you win the argument.