Below I have embedded a great video from SciShow Psych on the differences between female and male brain. I recommend it because Hank Green and colleagues have clearly read most of the relevant literature in the field.
The conclusion they come to is that although you may measure differences between the two biological sexes brain wise, it is unclear whether these differences have anything to say with men and women’s abilities, interests, or behavior.
It is also clear that if there are any clear differences, they are normally very small and only make sense on an aggregate level. That is: The individual male and female brains always display a mix of “femaleish” and “maleish” traits.
Hank Green does not discuss research into the brains of transgender people in this video. What his presentation tells us, however, is that it makes little sense to say that a trans woman is a woman because she has a “perfect female brain”. Given that there is so much variation between men and between women in this respect (a woman may have a brain that looks similar to the average “male brain” and still identify as a woman), being close to the female average neither confirms or invalidates her gender identity.