I used to work for company A  in India.I resigned from company A for joining another company B in India in my home town. I have got everything from company A such as experience letter,relieving letter etc.After working 4 months in company B,I realized that I am not good fit for this position with company B.So I contacted company A (my previous employer) for an opportunity.They offered me a position immediately and sent me the offer letter which I have accepted.Under such circumstances,I mailed my resignation to my current employer( company B) mentioning my last day which is after 2 months from the date of my resignation letter as my notice period is two months.But my current employer (company B ) did not accept my offer letter saying that they will give time to learn .But I really do not want to work in my current organisation as it is not at all good fit for me. Company A asked me to send resignation acceptance mail after one month from the date of issuing offer letter.As I do not want to loose the opportunity with company A ,I sent them a false resignation acceptance mail stating my manger's name of company B as approver of my resignation and last working day as 3 months after the date of offer made by company A as I get another 2 months time for serving the notice period after submitting my resignation letter again.
My questions are -
1)Can company A send the false resignation letter(which i sent to company A) to company B to check whether it is true or false?
2)If company A send the false resignation letter to company B,Can any of these two companies take any legal action or any other action 
against me?
3)What should I do now?
Please help.
Thanks.