You most certainly can, even in a State like Texas or Arizona.. To be safer and avoid any unnecessary hassles, just make sure to also carry some sort of government issued ID or passport on you, to be able to prove that you are in fact the individual mentioned on the appointment letter that has now been stamped by USCIS. Don't you also have the receipt of the I-485 on you? Better also take that one, as it is even more important than the biometrics receipt and shows you are pending adjustment of status.
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You can travel domestically with a valid government issued ID.
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Traveling within the U.S. is fine. You should keep receipts of your pending AOS application and any other documentation showing that you have permission to remain in the U.S. While you are away, make sure someone is checking your mail in case USCIS sends you information including a request for evidence. It is always best to consult an immigration attorney with these types of questions, particularly if you need to travel outside the U.S.
I believe you are free to travel within the United States while awaiting further processing of your filed and pending AOS case, however, I suggest carrying the copies of all official USCIS correspondence with respect to your AOS case, biometrics letter et cetera. DO NOT LEAVE THE US TERRITORY.
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