The thing is, if any adult woke up in the opposite sexed body a la Freaky Fridayesque event , of course they would still have the thought that they were their previous sex, because they had spent upteen years thinking the thought "I am female/male", however that is not feeling like a woman/man, that is thinking you are a women/man. The facts of the matter would be that despite still thinking of yourself as the opposite sex you would not be that sex anymore. Thoughts can be erroneous.
Now, would an adult be able to adjust their thoughts to fit the new reality? Probably quite difficult but as this is never going to happen, it's a moot point.
You can't feel male or female because they are not feeling states, they are material reality. People think they are female or male because their observable biology is named thusly. These names have been derived via a scientific method of observation (over millenia).
People with sex dysphoria erroneously think they are the opposite sex. It's likely that there are a myriad of causes as to why individuals think this way but if it is biological in nature then we should be able to identify and use biological markers in diagnosing people with sex dysphoria - so far, no such diagnostic tool exists.
If gender is in the brain then it should be observable - until it is shown otherwise, gender is a social construct that is hierarchical in nature.