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Democratic Front for the Liberation of Palestine was created in 1969.
National Liberation League in Palestine was created in 1942.
Popular Front for the Liberation of Palestine was created in 1967.
There is no organization that fits all of these criteria. There is no Palestinian/Arab/Islamic militant organization that was founded in 1817. However, a militant organization created in 1987 that rivaled the Palestine Liberation Organization and strongly opposed the Oslo Accords was HAMAS.
Afghanistan Liberation Organization was created in 1973.
Barbie Liberation Organization was created in 1993.
Tamil Eelam Liberation Organization was created in 1979.
PLO stands for Palestinian Liberation Organization, and the name explains the purpose for which it was created; to liberate Palestine from Israel. The PLO and Israel made peace in the 1990's, and since then Palestine has existed as a semi-autonomous state within Israel.
The Palestinian National Authority was established in 1994 as a result of the Oslo Accords between the Palestine Liberation Organization and Israel. It was created to govern certain areas of the West Bank and Gaza Strip.
The PLO was created in 1964. This is important, because most Palestinian apologists claim that Palestinian terror is a reaction to the 6 day war that took place in 1967. In fact, the tactic of terror became the weapon of choice for Palestinians and other Arabs after losing battles to Israel in 1948, 1956 and failing to find any other way to effectively injure Israel. The Palestinian terror model affects air travelers to this day. It was Palestinian terror hijacking that led to metal detectors in airports decades ago.
The Liberation Of... was created in 2008.
Liberation Records was created in 1994.