Surprise that your present employer had promoted you in-spite of you resigning from your post. You have mentioned that they have emailed you about your promotion. Forward that email to your personal id and take a copy of the same, if needed. This might also be a retaining strategy which they would have tried.
Or as Mahesh says, it may be a retention strategy.
In either case, why will they give it to you ? You are not staying, so why will they actually promote you.
There is no,legal basis to demand the letter, so forget it and move on.