All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
If the divorce was invalid as you were informed due to its being forged, then you are still in the guardianship of your former husband, and it is unlawful for you to marry another man before you leave him by divorce, Khul‘, or a court judgment given by a Sharee‘ah judge, and your ‘Iddah (Post-marriage waiting period) is over.
Based on that, your marriage from the second man is void and invalid under Sharee‘ah. But if you did not know that you were still in the guardianship of your first husband, no sin would be on you, and you would be regarded as having had intercourse while mistakenly believing that it was lawful, by which ancestry is proven, and ‘Iddah from him is due on you. It is also due on you to leave that man and wait until the judge gives you a final, irrevocable, unappealable judgment of divorce from the first husband, or that you reconcile.
But if you know and are fully certain that your divorce from the first husband is valid, and that his claim of forging it is incorrect, you have the right to marry another man, and your marriage is valid in the Sight of Allaah The Almighty; and the judgment given by a judge could neither make lawful what is unlawful, nor unlawful what is lawful, and then it is impermissible for you to enable your first husband to treat you as his wife.
Allaah Knows best.