The copy of the letter is in the Bible - Jer. 29. The time of the letter is soon after Hananiah's false prophecy which is dated.
(Jeremiah 28:1-4) . . .Then it came about in that year, in the beginning of the kingdom of Zed·e·ki′ah the king of Judah, in the fourth year, in the fifth month, that Han·a·ni′ah the son of Az′zur, the prophet who was from Gib′e·on, said to me in the house of Jehovah before the eyes of the priests and of all the people: 2 “This is what Jehovah of armies, the God of Israel, has said, ‘I will break the yoke of the king of Babylon. 3 Within two full years more I am bringing back to this place all the utensils of the house of Jehovah that Neb·u·chad·nez′zar the king of Babylon took from this place that he might bring them to Babylon.’” 4 “‘And Jec·o·ni′ah the son of Je·hoi′a·kim, the king of Judah, and all the exiles of Judah who have come to Babylon I am bringing back to this place,’ is the utterance of Jehovah, ‘for I shall break the yoke of the king of Babylon.’”
(Jeremiah 28:15-29:10) . . .And Jeremiah the prophet went on to say to Han·a·ni′ah the prophet: “Listen, please, O Han·a·ni′ah! Jehovah has not sent you, but you yourself have caused this people to trust in a falsehood. 16 Therefore this is what Jehovah has said, ‘Look! I am sending you away from off the surface of the ground. This year you yourself must die, for you have spoken outright revolt against Jehovah.’” 17 So Han·a·ni′ah the prophet died in that year, in the seventh month.
29 And these are the words of the letter that Jeremiah the prophet sent from Jerusalem to the remainder of the older men of the exiled people and to the priests and to the prophets and to all the people, whom Neb·u·chad·nez′zar had carried into exile from Jerusalem to Babylon, ... ... ... For this is what Jehovah of armies, the God of Israel, has said: “Let not YOUR prophets who are in among YOU and YOUR practicers of divination deceive YOU, and do not YOU listen to their dreams that they are dreaming. 9 For ‘it is in falsehood that they are prophesying to YOU in my name. I have not sent them,’ is the utterance of Jehovah.”’” 10 “For this is what Jehovah has said, ‘In accord with the fulfilling of seventy years at for Babylon I shall turn my attention to YOU people, and I will establish toward YOU my good word in bringing YOU back to this place.’