H1B visa transfer and travel

I have a valid H1B Visa from Employer A till Oct 2022. I am in India now and got an opportunity with different employer B. If I apply for consular petition from employer B being in India, do I have to go for stamping ? Or I can just carry Consular petition Receipt from Employer B and travel with my existing valid Visa?

You don’t need to if you have a valid H1B visa at the time you will travel to the US. Carry copy of complete I-129 petition along with approval notice, appointment letter and other supporting documents. CBP can issue the I-94 at port of entry.
Also its important to consult employer B immigration lawyer in case you need to carry any specific documents related to your case such as client letter etc.

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H1B cap exempt:

I have H1b under cap exempt category and is valid till July 2024. I’m thinking of moving from cap exempt to cap non exempt category employers. Since their is very limited scope for switching companies under cap exempt category. I would like to know the process of beginning this and what are the things that I should be aware of.

Also, second question I have perm filed with the existing employer, if I stay with present employer for 6 years, can i move to h1b cap non exempt employer by applying transfer or irrespective of 6 years timeline i should definitely get into lottery for sure?

is process going to be any different if I have I140 approved while switching from cap exempt to cap non exempt?