Question about the menu after the first "ending"

Hey all, just a quick question. I played through the game fully and after the first "ending" (the fakeout) happened after Nowhere, I always click "Begin" to continue. Since I want to play this section with a friend, I don't know what happens if you press "Quit" instead. I heard the game also goes to the memory Penrose section after, regardless of quitting or beginning. Is that true? Just so I know if I have to explicitly tell him to click "Begin", so he doesn't miss the rest of the game. Thanks in advance :)