This area was known as Southern Syria under the Ottoman Empire. It was the League of Nations that resurrected the pseudonym “Palestine”, and they actually did not give that name to Jordan, using “Transjordan” instead.
Even one of their earlier leaders, Ahmad Shukairy said in 1956 at the UN, Palestine is but southern Syria, nothing else.
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NYT, June 1, 1956
SYRIA SAYS IN U.N. PALESTINE IS HERS; History Cited by El-Shukairy —Eban ...
A el Shukairy asserts Syria’s historic claim to Palestine, s, UN Security Council; Eban says statement shows Syria’s expansionist designs...
http://www.nytimes.com/1956/06/01/archives/syria-says-in-un-palestine-is-hers-history-cited-by-elshukairy-eban.html