The MFA writes:
President Peres has previously sent two letters to the Egyptian president. The first was sent upon his election as president and the second was sent on the occasion of the month of Ramadan. In his first letter, President Peres congratulated President Morsy for winning the elections, emphasized the importance of peace between Israel and Egypt and expressed his hope for the continued cooperation between the two nations. In the letter, dispatched on 28 June, President Peres wrote: “As a person who participated in the process that led to the establishment of the peace agreement between your country and mine, I know that both Egypt and Israel attach supreme importance to the peace and stability that serve the interests of all peoples in the region. All of us in Israel respect both Egypt and the Egyptian people, which served as the pioneer that outlined the path to peace and reconciliation in the region. We know that the work is not yet finished. The people of Israel congratulate you on the democratic elections and hope that under your leadership Egypt will meet the complex challenges facing your nation. We look forward to continued cooperation with you, based on the peace agreements that were signed more than 30 years ago. It is our duty to preserve and nurture these agreements for the benefit of both our peoples. Peace has saved the lives of countless young people in Egypt and in Israel. Our commitment to the younger generation will always be valid. Unlike war, peace means victory for both sides.”
Prior to the Ramadan holiday, President Peres sent an additional letter of greeting to the Egyptian president, in which he expressed his holiday blessings to President Morsy and the Egyptian people.
UPDATE: Egypt denies sending this "telegram" and said that Morsi has not initiated any contact with Israel so far.
Maybe because it is a fax, not a telegram.