TCS will issue responsibilities letter only for people who resigned, and not for people who are actively employed.
Other option is to get the letter from a manager or co-worker, and have them notarized. It should include their official email id and phone number with country code. Submit that letter + their identity card. The colleague should have worked for the entire tenure in which you have worked in TCS because they would have to give an affidavit for your entire experience. It is fine if they have worked in different projects/locations/clients/teams etc. Just their tenure with TCS need to match your tenure. If your colleague has a Linkedin profile, make sure that it is up to date.
Write a explanation that since the company did not provide a letter, you got a notarized letter from manager/co-worker for responsibilities. If HR writes back in email saying that they won't issue the letter, include that as well for proof. It is fine even if they haven't given anything in writing. Just put an explanation, and you should be fine.
Also along with the letter include every other document that you have. Appraisal letters, promotion letters, tax returns, 6 recent pay slips etc. Even if it is overseas deputation, just include tax returns/pay slips of that you get from TCS in that country. Put everything in one PDF. Keep the first page for explanation, second page for index of documents, third page for actual letter from co-worker/manager with responsibilities, and followed everything in chronological order.. recent first.
I just listed what worked for me.
CIC is very liberal when it comes to reference letters from big companies and they don't expect it to be in letter head. But responsibilities letter is a must irrespective of any number of documents you provide. Without that CIC will not be able to confirm that you worked on your claimed NOC. No responsibilities document = no PR.
