This is the place where caliph Umar (may Allah be pleased with him) made salah after the Muslim conquest of Jerusalem in 638 AD. It is located opposite the Church of the Holy Sepulcher.
The Patriarch of Jerusalem showed Umar (may Allah be pleased with him) around the Church of the Holy Sepulcher, during which the salas occurred. The patriarch offered him a place for prayer in the church, but Umar (may Allah be pleased with him) refused, explaining to the Patriarch: “If I prayed inside the church, the Muslims who come after me would have mastered this, According to tradition, he took a stone, threw it on the street and prayed in the place where it landed. The current mosque of Umar (or Masjid-i-Umar) was built on this site by the son of Salahuddin Ayyub Afdhal Ali in 1193 AD
At a time when Muslims first conquered Jerusalem, Jews were expelled from Jerusalem and its environs by Christian rulers. Umar (may Allah be pleased with him) agreed with Sophronius (the Patriarch of Jerusalem) that the Jews would not be allowed to live, but later canceled this agreement. Umar (may Allah be pleased with him) invited 70 Jewish families from Tiberias to settle in Jerusalem, which allowed them to also build a synagogue.
Several prominent Companions of the Prophet (SAW) also settled in Jerusalem, attracted by the holiness of the city. Ubadah bin Samit (may Allah be pleased with him), one of the leading experts in the Koran, became the first Qadi (Islamic judge) in Jerusalem.
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A copy of the Testament, which was compiled by Umar (may Allah be pleased with him), gives security guarantees to the (non-Muslim) people of Jerusalem, is exhibited outside the mosque.
This mosque should not be confused with the Dome of the Rock, which is sometimes mistakenly called the mosque of Umar. Next to the Al-Aqsa Mosque, also known as the Umar Mosque, is a small mosque.
Video outside the mosque:
Sources: A history of Jerusalem – Karen Armstrong, Wikipedia, The Rough Guide to Jerusalem