During his royal tour, William will become the first official royal visit to Israel and the Palestinian territories.
Three decades of British rule between the two world wars helped establish some of the fault lines of today's Israeli-Palestinian conflict, and Britain's withdrawal in 1948 led to the eventual establishment of Israel and Jordan.
When he was shown the image of his wife and her family at the spot, William remarked that he would "need to come back with the family" to re-create it.
The duke's visit comes during a period of increased tension in the region.
The correspondence was included in Yad Vashem's Kindertransport exhibit, as well as in Foner's memoir, a copy of which he said he hoped to present to Prince William.
Prince William has toured the ruins of the Roman city of Jerash, walking in the footsteps of his wife who visited as a child when she and her family lived in Jordan.
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He was joined by UK's Orthodox Chief Rabbi Ephraim Mirvis during his visit to Yad Vashem.
The Duke of Cambridge is commemorating the millions of Jews who died during the Second World War on a visit to Yad Vashem, the World Holocaust Remembrance Centre in Jerusalem.
During the four-day visit, William is also scheduled to meet Palestinian President Mahmoud Abbas and Palestinian youngsters in the occupied West Bank.
Later in the day, the prince will see Prime Minister Benjamin Netanyahu and President Reuven Rivlin before heading to Jaffa and Tel Aviv on the Mediterranean coast to meet young people participating in a football-based youth programme.
Britain captured Palestine from the Ottoman empire in 1917 during World War One and administered the territory under global mandate until 1948, pulling out a day before Israel declared independence.
However, The Sun reported William said she loved her time living in Jordan as a child and commented, "we'll have to bring the kids next time". Jordanian Crown Prince Hussein recorded it for him, and the two watched it later Sunday on a huge TV screen at Hussein's residence.
Upon arrival, the British royal was welcomed by Jordan's Crown Prince Hussein. and it went beyond the formal setting.