Fr John Bosco Vincent Raj, SDB, from the Holy Land, tells me that Christians there do not usually use the expression SALAM ALEKUM, which is used commonly by the Muslims. At Easter the Christians say AL MASIH QAM, HAKKAN QAM - Christ is risen, truly risen!
In Arabic, the gospel text can be transliterated SALAMUN LAKUM, or else simply SALAM LAKUM.
The Jews use the greeting SHALOM ALEKEM. This is also the greeting of Jesus in the gospel text in Hebrew.