Is the Islam of a Christian girl who converted to Islam out of a desire to marry a Muslim accepted, and is a Muslim rewarded for marrying her with the intention of bringing her into Islam?

If a woman embraces Islam, her conversion is recognized, even if the reason for her conversion is her desire to marry a Muslim. This is because rulings are based on outward appearances, and Allah knows what is hidden. Indeed, Anas married Umm Sulaym to Abu Talhah after his conversion, and she did not ask him for a dowry other than his acceptance of Islam.