I want to say that that person is me. But then, precisely, I want to keep the pronoun in place to add some spice and power to it! Otherwise, better choices are... That person is me/that's me, I'm that 'he' etc.
The context (hypothetical) is someone unknowingly describing 'he' and then I reveal that I'm that 'he'.
"Yeah, I know she is mad in love with someone whom I have never seen. And you know what, he is very mysterious. I have heard that he practices black magic as well. At times, she behaves that someone has doggoned her. Do you know him?"
And I reply cunningly...
(chuckling) I am he/him.
I lean toward him. As we say... "...hey...see there...that's him"
But Jesus says... I am he!.