The Müllerian duct develops into:
Müllerian ducts also called paramesonephric ducts arise alongside Wolffian ducts in both sexes during early fetal development. In absence of anti-Müllerian hormone as in female embryos, ducts persist, fuse caudally and differentiate under estrogen and Wnt signaling into oviducts, uterus, cervix and upper vagina; unfused cranial portions become Fallopian tubes. In males AMH secreted by Sertoli cells induces regression via apoptosis preventing female organ development, while testosterone maintains Wolffian derivatives forming epididymis and vas deferens. Therefore developmental fate of Müllerian duct is female internal genitalia.
Ref: Gilbert, Developmental Biology, 12th ed., Chapter 17: Müllerian duct develops into female internal genitalia.