Mr Darcy did not give a letter to Jane.
He did give a letter to Elizabeth the morning after he proposed and she rejected him. The purpose of the letter was to defend himself against accusations she brought against him when she declined his proposal.
Chat with our AI personalities
Darcy tells Elizabeth the history of his relationship with Wickhmam. This includes that Wickham had tried to elope with Darcy's sister, Georgiana; that Wickham had refused to take the parish offered him by Darcy's father, and other, minor information.
Darcy also admits that he had separated Bingley from Jane and that he had not told Bingley that Jane had come to London. He makes no apology for this.
He told her the true nature of his relationship with Wickham, he admits having influenced Bingley into running away from Jane and he explains his haughtiness and his objections to some of her close relations.
Mr. Darcy gave Jane a letter in chapter 46 of Jane Austen's novel "Pride and Prejudice." In the letter, he explains the reasons behind his interference in Jane's relationship with Mr. Bingley and confesses his feelings for Elizabeth Bennet.