Praise be to Allah.
It is well known in the religion of Allaah that it is forbidden to follow in the footsteps of the Shaytaan, and that all the steps that may lead to falling into something haraam are forbidden, even if they are permitted in principle. This is what the scholars call “preventing the means (that lead to haraam).”
The basic principle of sharee’ah is that when Allaah forbids a thing, He also forbids the ways and means that lead to it, so that it may indeed be forbidden.
We are happy when we hear of or see someone who has come back to Allaah and to His religion after having lost their way, but at the same time we fear that the Shaytaan may make what they used to do when they were astray attractive to them, thus preventing them from following guidance and making them go astray again.
Obviously this is what we fear for the sister who asked this question and for her former friend who has also repented. Hence we cannot condone her idea of getting back in touch with the one with whom she had a relationship before she was guided, even if that is on the basis of wanting to get married according to sharee’ah.
For a non-mahram woman to be in touch with a person with whom it is not permissible for her to be in touch leads to evil consequences which are obvious to any wise person. Hence Allaah has forbidden establishing relationships and taking close female friends. We have already posted some of the fatwas of the scholars on this issue. See questions no. 23349, 20949and 10221.
With regard to the answer to your question, which may be summed up as: Is it permissible for a woman to propose marriage to a man or to tell him that she wants to marry him? The answer is that in sharee’ah the word khutbah (proposal) refers to the man asking the woman. See question no. 20069.
If a woman wants to marry some man, there is nothing wrong with her sending someone whose religious commitment and honesty she trusts to offer her in marriage to him, as Khadeejah (may Allaah be pleased with her) did when she heard of the Prophet (peace and blessings of Allaah be upon him) and saw his good attitude and trustworthiness, and wanted to marry him. So she sent one of her relatives to offer her to him in marriage, and he agreed to marry her.
Based on this, we say to the sister who asked this question: If you want to marry this young man, and he has a good attitude and is religiously committed, then there is nothing wrong with suggesting marriage to him through a trustworthy relative of yours.
You should avoid getting in touch with him or with any other non-mahram men, because of the fitnah (temptation) involved in that.
And Allaah knows best.