Haman is an important person in the Qur'an, who opposes Moses and his message together with Pharaoh. The Qur'an mentions Haman six times: al-Qasas 28:6,8,38; al-`Ankabut 29:39; al-Mu'min 40:24,36.
Non-Muslims easily recognize that the person of Haman in the Qur'an as a reflection of the biblical Haman in the book of Esther. Haman's occurrence in the story of Moses and Pharaoh of the Qur'an has long been a prominent charge of a historical error in the Qur'an.
A detailed discussion of the Haman in the Qur'an and the similarities to the biblical Haman, see these articles:
In 1994, Dr. Maurice Bucaille published a book with the claim that the name Haman was found in an old Egyptian inscription, implying the superior historical accuracy of the Qur'an over the Bible. Soon, the "miracle of Haman" became one of the most prominent proofs Muslims used to convince themselves and others of the divine origin of the Qur'an. Various Muslim apologists developed variants of this argument.
The main Muslim versions of this argument are discussed in great detail in this article series:
Another attempt to anchor the quranic Haman in history was proposed by Sher Mohammad Syed in 1980. His hypothesis has not gained much support (compared to Bucaille's claims), but is still cited here and there and has been republished twice. It is evaluated in this article:
After the above rebuttals, Islamic Awareness changed their argument. Their new approach is examined here: