The Consequences of Forgery in Employment
Destiny beckons! Your acceptance in writing is a mirror to the documents you forged. Good news, you are aware of it. Bad news, the HR in that firm is now as much at fault as you are. Keeping a written acceptance of the forgery is a double-edged sword as it unmasks the HR as a scheming one. Your acceptance in person was enough. Making you write it down shows pettiness and scheming on their part!
Moving Forward After the Incident
What matters to you now is what lies ahead. You will put this job behind you and obviously never mention it in any of your resumes in the future. Please consider not using any reference from this firm. Human nature is prone to gossiping. This incident might fuel the grapevine. Choose to stay as far away as you can.
Ethical Considerations and Verification
I know this doesn't sound very ethical. If you still doubt, try to get a reference check done on yourself using this firm's letter. There are companies with whom you can initiate your background verification. You would have to pay the fees, but that would answer all your doubts. You can even request to keep the reason for the verification private, where they will not share with any of your ex-employers why your credibility is being validated.
Impact on Future Prospects
How does the acceptance affect your future? To begin with, it doesn't, unless you registered for this job with Skill Registry in Nasscom. At most, this would be stored as a comment on the reason for leaving in the company MIS/Database.
Individually, this incident has definitely changed you as a person. Sooner rather than later, you will be on the other side of the table where you will be dealing with ambitious talents who would think twice before risking all they have. You might deal with it differently, for you understand the price of this risk.
Wishing you all the best!