What is the ruling on delaying Fajr prayer until Duha due to the difficulty of performing ghusl for janabah at night after intercourse?

What you are doing by delaying ghusl (definition) al-janabah (definition) (ritual bath after sexual defilement) and Fajr prayer until Duha (forenoon) is forbidden (haram (definition)), and you must repent and seek forgiveness. If there is a legitimate shar'i excuse preventing ghusl, then you must perform tayammum (definition) (dry ablution) and pray on time. It is not permissible to delay prayer due to lack of purity, and whoever does so has disobeyed their Lord. The solution is to promptly perform ghusl and pray before the time expires, or perform tayammum and pray if ghusl is not possible.