Jack scoffed. "Teach me to drive - muggleborn, remember? My little beater car just took too big a beating. Been on bed rest for the past few weeks until I get it a new alternator belt." She smirked, keeping her eyes on all the knobs. "I just saw a spy film where one of these government tricked-out SUVs had knobs that triggered cool gadgets. I know it's not likely, but I'm not gonna leave saying I didn't try." She twisted the last of them and sighed, sitting back. "Bloody shame."
Jack smiled to herself at his words - he so obviously cared for this woman. She pondered the question - this woman wasn't really a threat. She wasn't against England, she was against aging. Jack's view of right and wrong could be rigid, but she knew a criminal from a woman facing her mortality. Azkaban was not going to stop her. She would only be more determined to prove herself, and would attempt to leave, or kill herself doing that.
That's why it made perfect sense to...
"Place her in the Department of Mysteries," Jack said. "Either trick her into thinking she's doing it so as to make a buck or whatever, and put her in an impossible room she could work on every day, or get her to work there. Criminal studies, yeah? Close enough to you so she won't have to pull off major stuff, but enough to do to keep her busy."