From Marshall, Sinai Victory:
What is called "Parker's Memorial" in this book, and is herein pictured, is described in a reliable source as a monument to the memory of Col. A. C. Palmer, DSO, a valiant British officer who was twice governor of Sinai. But the troops who went there insisted on calling it "Parker's Memorial" however it was dedicated, and they certainly knew where they were going. The late Colonel Palmer should not mind that, in rehallowing the spot, they were a mite careless about its name.
So, who was Colonel Palmer and what is the memorial about?
(And is the monument still there or what happened to it?)
Edit: Hebrew wikipedia has some answers (spelling regularised):
The Parker Monument [was] a monument to the memory of Colonel Alfred Chevalier Parker, which was built in the 1920s at the eastern entrance of the Mitla Pass in Sinai, Egypt and was destroyed by Egypt after Israel's withdrawal from Sinai in 1957. [...] Colonel Parker was the British governor of Sinai in the years [1907-1912], and 1918-1923[.] The [monument] was erected at the eastern entrance of the [Mitla] pass by Parker's successor as governor of Sinai, Claude Jarvis, since Parker was the one who initiated the construction of the stone road in the sands from [El Shatt] to the western entrance of the [Mitla pass.]
And: the name Palmer may be a confusion with Edward Henry Palmer, who was murdered in the area, as noted in comments.