The Prophet, sallallaahu 'alayhi wa sallam, did not send a letter to the St. Catherine Monastery
22-9-2013 | IslamWeb
Question:
Assalamualikum. Is the Prophet's letter to St. Catherine of the below link authentic? http://www.ijtihad.org/Prophet%20Muhammed%27s%20Promise.htm
Answer:
All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
There is no basis for that letter. It was not mentioned in the books of Sunnah nor the books of history. There is no Islamic source for it; in addition to the clear difference in its style and meaning from the letters of the Prophet, sallallaahu ‘alayhi wa sallam, to the kings, princes and delegations.
Shaykh Bakr Abu Zayd said in his book Al-Ibtaal li Nathariyyat Al-Khalt Bayna Al-Islam wa Ghayrihi min Al-Adyaan: “Christians have forged the document of St. Catherine hanging in the monastery of Toor Sinai. It is a false document that Christians have written. Also, in Majallat Ad-Daarah (Ad-Daarah Magazine, ed. 3 for the year 1400, p. 124-130), there is an important research explaining some of the documents that Jews and Christians have forged and amongst them is that document. In addition, amongst the evidences of forging it is stating the witness of Abu Hurayrah 
on it while he embraced Islam in the year of Khaybar 7 A.H. while it is dated in the second Hijri year!”
As for the known letters of the Prophet, sallallaahu ‘alayhi wa sallam, to the people of Egypt, it is his letter to Muqawqis, Ruler of Egypt. Ibn Al-Qayyim 
said in Zaad Al-Ma‘aad: “The Prophet, sallallaahu ‘alayhi wa sallam, wrote a letter to Muqawqis, King of Egypt and Alexandria saying: “ In the name of Allaah, the Entirely Merciful, the Especially Merciful. From Muhammad, the Slave and Messenger of Allaah to Muqawqis, the leader of Copts. Peace be upon those who follow the right path! I invite you to Islam. Embrace Islam so that you will attain salvation. Embrace Islam so that Allaah will reward you twice. If you refuse my invitation, you will be responsible for the sins of Copts.{Say, “O People of the Scripture, come to a word that is equitable between us and you - that we will not worship except Allaah and not associate anything with Him and not take one another as lords instead of Allaah.” But if they turn away, then say, “Bear witness that we are Muslims [submitting to Him].”} [Quran 3: 64].”
Allaah Knows best.