Here are the answers to the best of my knowledge:
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Normally, what I have seen is that TCS has a clause in their agreement with client that they cannot directly hire their employees for 6 months after they leave TCS. Now, it depends on what contract they have with your company. But, normally, this is the trend followed by all big Indian IT companies.
Your client (who is offering this job) would know more about what they have signed on with TCS. -
Yes, it would be a breach of contract with TCS if you do not serve full notice period. But, there are ways to solve that issue as I have mentioned above in the article. You can always buy out the notice period if you do not want to go back to India and serve full notice period.
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No, this whole thing will NOT affect your green card process in any way. the only thing to keep in mind is that you should complete the full and final settlement with TCS after you leave the company. This would help you get the Skill letter and experience certificate that’s required in GC labor processing.
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I have seen people moving from TCS to client they were working for, with no issues. It depends on TCS to challenge that move based on the contract with client. Normally, they don’t do it primarily to avoid any sourness in the relationship with client. But, remember, this is my personal opinion and may or may not be true. the risk is always there.
I hope I answered all your queries. Let me know if you need more information.