There is a coat of stencil paper (carbon copy) inside the envelope. He inserts a blank sheet of paper inside (when he has his hands behind his back, he only pretends he's writing something), and waits for the woman to pick a letter. He then quickly writes the letter either with his nail or a pocket writer on the outside of the envelope (see how he holds the envelope in a weird way at 0:28), which transfers to the sheet of paper. He can then hand out the envelope to the participant and... Prestige!
Here's a typical pocket writer (this one is more often used while fumbling in a pocket):
https://kranzomagic.myshopify.com/produ ... nger-style