COS J2 to H1b (including the i-94 patch)

Hello, I just finished the H1B process with a change of status within the US.
I got the small i-94 patch on my I-797A and was told by the lawyers that I don’t need a visa stamp and I can go in the US with the small i-94 patch.
Is this right? I had the impression that I have to get a visa stamp. If so, do I need to do it outside of the US even if I got a COS approval?
Thanks

Yes.

Visa is only required if you leave the US and want to enter back on the non-immigrant status you are currently in. If you have no plan to leave the US, you are all set and do not need a visa stamp.

Your status while in the US is governed by the I94 and you can keep living and working in a H1B job till the expiry of I94.

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