Try this logical argument, as she sounds like a bright girl.
Any criminal who gets shot and dies will go to Hell as a result of the way he/she chose to live. God gave us all free will, and the criminal made choices using that free will. While you and I chose to live good lives, this criminal chose to live a bad life, victimizing others. If a bullet from my gun kills the person, I did not sit in judgment of the person's life. God did. And if God chose to send the criminal to Hell, that is God's will. My role, to paraphrase the often used quote, was simply to arrange the meeting. The same as if the criminal had drowned, overdosed on drugs, been hit by a car, or simply went to sleep only to have his/her heart stop somewhere in the night. While I may be responsible for the death in this example, the eternal suffering as you call it is his/her consequence for a lifetime of sin.
Besides, which is the better outcome, that this criminal suffers for his sins, or that myself or some other person, or many other persons should suffer as a result of the criminal continuing to live and victimize others?
Good discussion with a young lady looking for answers in a world full of questions.