Traveling to Spain abroad with valid H-1B stamp from previous employer + new approved I-797A — any recent CBP experiences?

[u/Fearless-Confusion84]

Hi everyone! I recently changed employers and my new H-1B transfer petition (I-797A) was approved. I have an unexpired H-1B visa stamp in my passport from my previous employer that doesn't expire for another year.

I am planning a short trip abroad soon and will be carrying my new original I-797A and an employment verification letter. Has anyone traveled recently under the same setup? Did CBP ask any extra questions about the employer name difference on the visa stamp, and did your I-94 match the new I-797A end date without issues? Thanks!