Switching from TN to H1B

We're family of Canadian citizens. I am on TN and my family on TD. I got my i-797A (approved for change of status) for H1B. I plan to go to the border along with my family to get the status updated from TD to H4.

a. Do I need to carry any documentation or my approved i-797A enough?
b. Does my family need any documentation other than proving the relationship?

thanks
 
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My family did this back in 2018, TN/TD to H1B/H4. We were in Southern California so we drove to the San Ysidro Ped West POE near San Diego.
I brought the original i-797A, copy of the H1B petition, passports, original long form birth certificates, marriage certificate, Canadian Passports.
I paid $6 for each I-94 card, we were photographed, fingerprinted and officially entered the US on H1b for myself and H4 four spouse and dependent. Passports were stamped and new I-94 cards issued. The CBP agent had to ask his supervisor for assistance as it is not very common for TN/TD to H1B/H4 at this POE.
The agent did not ask for the H1b petition, but my employer provided it to me just in case.
Other than the 2+ hour wait in line, it went smoothly.
 
I didn't get a copy of H1B petition from my employer as my approval was for change of status from TN to H1B.......


Did you go on a working day or a holiday?

thanks
 
I went on a Saturday.
My approval was also a change of status from TN to H1B. As I mentioned, by employer gave me a copy of my H1B petition, to take with me, but it was not necessary. The CBP did not ask for it. The i797A approval notice was all that was needed.
 
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