There are some similarities between the old Muhammedan Calendar and Umar's Hijri Calendar visible even today despite some position changes. For example the month names: Sivan/Ṣafar (Gemini), Elul/alŪlā (Virgo), Cheshvan/Shaʿbān, and Shevat/Shawwāl. Also, the major Hajj of the year is in the originally spring month of Dhū al-Ḥijja exactly like Passover in Aviv (spring). This is followed by the fasting of Iyyar/Muḥarram (Taurus) commemorating the deliverance from Egypt. Moreover, the 7th month is still sacred in both. Finally, Ramadan corresponds to the Julian Calendar's month of December of course.
It is therefore also known that Dhū al-Ḥijja corresponds to what is now March in the Julian Calendar, Muḥarram corresponds to April in the Julian Calendar, Ṣafar corresponds to May in the Julian Calendar, and the 7th month corresponds to September in the Julian Calendar.