Is a man's marriage to a woman who claimed her absent husband had died, based on a forged death certificate, then it later became clear that the husband was alive, considered a valid marriage?

If a woman brings false witnesses to prove the death of her husband, she has committed a grave evil from which she must repent. Your marriage to her is invalid, even if a Sharia judge ruled it so, because a judge's ruling does not change reality. She is still under the conjugal bond of her husband. You must separate from her, and you must verify such matters carefully in the future. We advise consulting the Sharia court.