May I share a bit about my own experience at this point?
I rather unwillfully became part of a "prison" ministery not by choice, but because the Lord allowed my youngest son to end up in a prison for almost three years. Until then, I knew nothing about it, and although he himself is not yet converted, he had plenty of Christian witness there. He also knew who the hypocrites were as well as the sincere ones, by comparing them to the walk of his committed family members! His one "Christian" exposure that he told me about was a rock band that came in to perform. Praise God they lost the electicity from a storm so that was cut short! That was not the type of witnessing I wanted him to have.
I now correspond with two truly converted inmates, and one who is not. The unsaved one was my son's last cellmate, and we had the common ground of being artists. He is polite, educated, articulate, and serving a life sentence.
To make a long story short, between all of them, there is no lack of the gospel in these places. Even Joseph, who is a practicing Bhuddhist, knows much of Christianity and our discussions prove it.
The litmus test is the new creation. I know Joseph enough that when he is saved, he will be a different person than the one I converse with now. The other Christian brothers say that prayer, kindness, and being there for them is the most valuable thing they need. It might take years before this bears fruit and Ty and David insist that I not give up and be the friend and mother that he needs as both of his parents are dead. Most of them have no family contact at all.
I stick only to the ones that the Lord has put in my life and believe, even as his life is unraveling now, that he will be saved.
Back to "knowing" that they are converted, we have the Word of God as a plumbline just as we do for those in the world that profess to know Jesus. Many say it, but their works say the opposite.
Both of the Christian brethren tell me that you have a majority of men that attend these meetings simply for something to do and not because they want the Lord. With this in mind, it is easier to understand the lack of sincerity in many of them. The key is to pray for them and that eventually they will see their need for Jesus too.
The few godly men I know and have met in the prisons, put many of us to shame. Twice, when I was visiting my son, there were inmates preaching to their loved ones. One young man that was sitting right next us outright asked his mom how often she read her Bible!
So, I hope this enlightened a bit and maybe answered a few questions. These men live on the brink anyhow, and we often jump in and perceive that we will turn the place upside down. I would pray to be in contact with those that are committed, and they will give you the best advice you can get to reaching their cellmates and thereby seeing the fruit you desire.
God bless.