H-4 to H1-B with H1-B amendment

Hi…for family reasons, I got my H4 stamped and travelled to U.S last month when I had an approved H1-B. Later I got a project and my LCA transfer is now completed and I got the certified LCA. I am not sure whether H1-B amendment is done. Is it mandatory - I will be working in a different state than my original LCA location filed while filing H1-B?

Also, I have a question on the ability to start working on H1-B. If I have the I-797A and I-797C along with certified LCA, can I start working (using I-94 of H4) or do I need to do any other process so as to be able to start working?. What are my options to start working without having the need to get H1-B stamped?

Appreciate your help.

Yes, it is strongly recommended to get H-1 amendment done.

Your latest I-94 is for H-4, right? So you need to have COS filed from H-4 to H-1. Once approved, you can start working on H-1 and start getting paid. You don’t need to get H-1 visa stamped in the passport as long as you continue to stay inside US on approved COS and valid H-1 I-94.