Did Jesus write a letter to King Abgar of Edessa?

One gets to read in [National Catholic Register](https://www.ncregister.com/blog/is-the-legend-true-did-jesus-write-a-letter-to-king-abgar) , the text of a letter alleged to have been written by Jesus in response to the letter from King Abgar of Edessa requesting the Lord to heal him : > Blessed are you who have believed although you have not seen me. For it is written concerning me that those who have seen me will not believe in me, and that those who have not seen me will themselves believe and shall be saved. But regarding what you wrote me, to come to you, I must fulfill all things for which I was sent, and, after thus fulfilling them, be taken up to Him who sent me. And when I have been taken up, I shall send you one of my disciples to heal your suffering and to give life to you and those with you.”. I wish to know if the Catholic Church has made any formal study on the said correspondence reported to have been made between King Abgar and Jesus ?