Of course, threading a needle is not too difficult. But who will be able to do it without looking, holding his hands behind his back? Perhaps anyone. But you can do it, and demonstrate to the audience: in one hand thread and the other with the needle, his hands behind his back, a little effort - and before all already the needle inserted into her thread.
Actually no special skill is required. The secret is simple. Of course, you prepared a needle inserted into her thread and hid it, sticking, say, the back of the jacket. Showing focus, you just pull it and demonstrate to the audience. It remains only to hide the empty needle, and from the thread that you had in hand, to get rid of.