All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
We thank the questioning sister for her aspiration to bring good for her sister. The Prophet said: “(The basis of) Religion is (sincere) advice.”
There are many ways to offer good advice to this sister. The questioner may give the sister a good lecture cassette that warns of the evils that are committed by sisters; or she may give her a pamphlet, a Fatwa, etc. This way she may avoid the feeling of embarrassment that is bothering her.
One should know that exchanging e-mails, or letters, etc., with the opposite sex is not permissible since most likely it is a channel that leads to Zina (fornication or adultery). Generally, such contract gradually leads to affection and love letters; thereafter, to the exchange of personal pictures as happened to the questioner's friend. Eventually, this practice urges them to have phone contact and finally to forbidden meetings. Allah has forbidden any means that could lead to Zina; for this reason He Ordered both sexes to lower their gaze, prohibited women to be soft in speech lest the ill motivated would become interested in them. Moreover, He Ordered Muslim women to wear Hijab, etc.
Every means that could lead to Zina is forbidden. No doubt, correspondence is the first step that ends up in Zina. Allah Says (what means): {…and do not follow the footsteps of Satan. Indeed, he is to you a clear enemy.} [Quran 2:168]
Allah knows best.