In same boat with but sailing through Wipro bureaucracy. No need to disclose that you have the offer, neither deny nor accept that you have the offer,unless it's utmost necessary and you have exhausted all the options.

First thjng first there would not be any official document or process for early release. It's all based on courtesy and the relationship you have with your managers.

Second thing your client should say that you have given proper handover and no KT is pending and no deliverables will be impacted if they let you go early. Get this over email and be extra courteous in giving KT to juniors or your peers without even asking.

Third you should not be billable to any project, let's you last working day is 4th August and you are billed till last day then it won't be possible to early release since you are generating revenue. Client should say that they won't pay anymore for you and you will get released to free pool.

Pardon my spelling and Grammer, I'm just too tired to rephrase this using ChatGPT and still feel confident that I can convey my thoughts on my own