Feisal was given Damascus by the British, but as you noted the French had a problem with that. Feisal was then set up in British-created Iraq. The third brother [Abdullah] was installed in [British-created] Transjordan, and that is the lineage which survives today.
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Kings of the Hijaz (of the Hashemite dynasty):
HM Hussein ibn Ali, Grand Sharif of Mecca 1908 (see above), upon his proclamation of independance King of the Arabs 29/10/1916-renounced the title 6/11/1916, King of the Hijaz 6/11/1916-abdicated 3/10/1924, Caliph al Islam 11/3/1924, °1853 or 1854, +Amman 4/11/1931 (bur Jerusalem), X 1 Mecca Sharifa Abdiya, d of Abdullah ibn Mohammed, Grand Sharif of Mecca, 2 1894 Abdila, °1879, + Cyprus 1930, daughter of Salih Bey. Father of (by Sharifa Abdiya):
HM Ali ibn Hussein, King of the Hijaz and Grand Sharif of Mecca 3/10/1924-abdicated 19/12/1925, °Mecca 1879, +Baghdad 14/2/1935, X Constantinople 1905 or 1906 Sharifa Nefissa, °Constantinople 1886 or 1887, +Baghdad 14/7/1958, daughter of Abd al Ilah Pasha, Grand Sharif of Mecca
Emirs then Kings of Transjordania, then Kings of the Hashemite Kingdom of Jordan:
HRH (1916) then HM (1946) Abdullah I ibn Hussein, Emir of Transjordania 1/4/1921-25/5/1946, then King of Transjordania 25/5/1946-17/6/1946, then King of the Hashemite Kingdom of Jordan 17/6/1946-20/7/1951, °Mecca ../11/1881, +Jerusalem 20/7/1951, son of HM Hussein ibn Ali, Grand Sharif of Mecca, King of the Arabs then King of the Hijaz, (see above, Kings of the Hijaz), X 1 Constantinople 1904 or 1905 Sharifa Musbah, °Mecca 1884 or 1885, +Irbid, Jordan 15/3/1961, daughter of Emir (Pce) Nasser Pasha and great-granddaughter of Grand Sharif Mohammed ibn Abd al Muin ibn Aun, 2 Souzdil, titled HH Pcess Souzdil, +Amman 16/8/1968, 3 ... Father of:
HM Talal ibn Abdullah, King of the Hashemite Kingdom of Jordan 20/7/1951-deposed for health reasons 11/8/1952, °Mecca 26/2/1909, +Istanbul 8/7/1972, X Amman 27/11/1934 Sharifa Zein bint Jamal, titled HM Queen Zein, °Egypt 2/8/1915, +Lausanne 26/4/1994, daughter of Sharif Jamal Ali ibn Nasser and great-great-granddaughter of Grand Sharif Mohammed ibn Abd al Muin ibn Aun. Father of:
HM Hussein ibn Talal, King of the Hashimite Kingdom of Jordan 11/8/1952 (enthroned 2/5/1953) - 7/2/1999, GCVO 1953, hon Air Chief Marshall, Royal Air Force 1966, Royal Victoria Chain 1966, Hon Degree at New York Univ 1996, educ al Alieh School in Amman, Moslem Lycée in Amman, Harrow School, Victoria College in Alexandria and Royal Military Academy in Sandhurst, °Amman 14/11/1935, +Amman 7/2/1999 (bur Royal Cemetery of Amman), X 1 Amman 19/4/1955 (div 1957) Sharifa Dina, titled HM Queen Dina 1955-1957 then HRH Pcess Dina from 1957, °Cairo 1929, (X 2ndly 10/1971 Assad Abd ar Rahman, °1935), daughter of Sharif Abd al Hamid ibn Mohammed and of Fahria Brav, great-granddaughter of Aun ar Rafiq, Grand Sharif of Mecca, 2 Amman 25/5/1961 (div 1972) Antoinette (Toni) Avril Gardiner, renamed Muna al Hussein on her conversion to Islam, titled HRH Pcess Muna 30/1/1962, °Chelmondiston, Ipswich, Suffolk, England 25/4/1941, daughter of Col Walter Percy Gardiner, MC, and of Doris Elizabeth Sutton, 3 Amman 24/12/1972 Alia Baha ed Din Toukan, titled HM Queen Alia al Hussein, °Cairo 25/12/1948, +Amman 9/2/1977, daughter of HE Bahauddin Toukan, fmr Amb of Jordan to London, 4 Amman 15/6/1978 Elisabeth (Lisa) Halaby, renamed Nur on her conversion to Islam, titled HM Queen Nur al Hussein, Dir of Planning and Design at Alia, the Royal Jordanian Airlines 1977, BA Architecture and Urban Planning at Princeton Univ 1974, President of King Hussein Foundation, °Washington DC, 23/8/1951, daughter of Najeeb Elias Halaby, fmr Chm of the Board, Pres and CEO of Pan American Airways and of Doris Carlquist
HM Abdullah II, King of the Hashimite Kingdom of Jordan since 7/2/1999 (see above, Head of the Royal Family)
http://www.almanach.be/search/j/jordan.html
Following a plebiscite with 96% in favour, Faisal (I) ibn Husain, formerly King of Syria, son of Husain ibn Ali, King of the Hijaz and descendant of the Grand Sharifs of Mecca, was proclaimed King of Iraq in 1921. The British protectorate was softened in 1922 and in 1925, leading Iraq to full independance in 1927. King Faisal I’s grandson, King Faisal II, was assassinated at Baghdad in 1958 and Iraq became a republic.