This is not a big deal. Just want to let people have some idea. Before I left, I asked but no one provide any info.
I switch from F1 to H1 in US, so only have H1 approval notice, not the real visa. After got AP, I consulted with our international officer, and he confirmed with CIS that AP alone is enough.
To cut story short, when leaving US, I hand in I94 from both old F1(stapled on passport) and H1 approval notice to the airline crew.
I come back from Shanghai Pudong, when check in, the airline crew ask for visa, and I showed the AP, no problem. Same at the Chu Jing exam.
After I landed in LAX, did NOT go to the visitor (or US passport holder, obviously) lines, there was a Seaman/Parolee line, line 17 when I arrived. The line was very short, usually only a couple of people. The DHS officer there handled AP case right there, I did NOT go the secondary insprection. I did bring with me I140 approval notice, I485 receipt notice and the H1b approval notice. But seems he just gave a quick glance. He did ask for my parent's name, probably just to confirm I am the person the application in the first place. Other than that, nothing, not even driver's lisence etc. I saw there was a checking list on his desk, under Parolee, about 6-7 items to go thorough. Total time is about 10 mins. No stress, and move very smoothly.
P.S. I did have some beef jerk and other food items (all in package, nothing raw) in my luggage, and the customer officer only asked "any food item?", I lied "No', and I was out onto the street. From landing to out to waiting area, 1 hr. I am even faster than those flight attendent!! Haha.