Praise be to Allah.
You should note first of all that the letter which came to you by mistake may have been fabricated against this girl.
Secondly, if you are sure that this letter is genuine, then one of the two following scenarios must apply:
1 – That this girl has started to change and reform, and she has ended her haraam relationships. In this case there is nothing wrong with your brother marrying her. You should cover up for her, because the Prophet (peace and blessings of Allaah be upon him) said: “The Muslim is the brother of his fellow Muslim; he does not wrong him or let him down. Whoever meets his brother’s needs, Allaah will meet his needs, and whoever relieves a Muslim of some worldly distress, Allaah will relieve him of some of the distress of the Day of Resurrection. Whoever covers a Muslim (conceals his sin), Allaah will cover him (conceal his sin) on the Day of Resurrection.”
Narrated by al-Bukhaari (2310), Muslim (2580).
The Prophet (peace and blessings of Allaah be upon him) has told us that repenting from sin erases it. He (peace and blessings of Allaah be upon him) said:
“The one who repents from sin is like one who did not sin.” Narrated by Ibn Maajah, classed as hasan by al-Albaani in Saheeh Ibn Maajah, 3427.
2 – If this woman’s religious commitment and character are not satisfactory, or there is no guarantee that she will not go back to haraam ways, then you should advise your brother not to marry her, because the Prophet (peace and blessings of Allaah be upon him) said: “Religion is sincerity (naseehah).” We said: “To whom?” He said: “To Allaah, to His Book, to His Messenger and to the leaders of the Muslims and their common folk.” Narrated by Muslim, 55, from the hadeeth of al-Tameem al-Daari (may Allaah be pleased with him).
That should not be done by accusing her or exposing her, rather it should be done by trying to divert your brother from marrying her, such as by sending him a letter or telling him directly that marrying this girl will do him no good. If that does not put him off marrying her, then you should tell him that you know something that means that he has to forget about marrying her, and other things that will make him give up the idea of marrying her, even if you are forced to tell him what happened with this letter, without slandering her.
And Allaah knows best.