Can a man still be a man with female genitalia?

If he identify as a man, then yes.

Yes - your gender is not determined by your genitals, even your sex isn't solely determined by genitals. The idea that you're only a man once you take hormones or change your genitals is false, as is the idea that you are only a male if you have a penis: sex determination is far more complex than this.

This is what is known as transgender - that is, you are born with one gender but on the inside you feel like the opposite gender. In this case, you would be considered female unless you undergo the surgery to fully transform into a male. However, it is possible for you to live as a man and say you are a man and even take hormones that make you appear more masculine without actually becoming a literal male.