My son-in-law got his AP today, He e-filed on March 20 and his approval was May 8 (for him this was a quick process, now if they could just get the background stuff done and send his green card). I am very happy for him, they had to save for almost 2 years so he can go back and see his mom and family. My question is that they sent him two identical documents I-512L, does he need both when he travels? He applied for travel once, but it says multiple applications, I am wondering if they take it each time he re-enters? Anyone have experience with this? And what line would he go to when re-entering?

I think they will take one when he enters the US and one he keeps! So it is normal to get 2.

My K1 wife is returning from Spain on Wed with her AP docs, so then I will know for sure. But Im pretty sure that they will keep one and return to other, and stamp your passport with the parole stamp. Each trip afterwards, she just shows the AP doc and they just log it as returning again.

Yep.. that's how it goes... except sometimes, they don't keep the other copy.. some of the time, they only stamp one and make a photocopy of it... so you'll have one endorsed I-512 and one blank I-512. In this case, the blank I-512 is worthless and you can make it into wallpaper if you want...