Stealing and lying and inability to learn from consequences are common in kids with FAS disorders. These are all part of the neurological dysfunction that is a result of damage from alcohol exposure, especially to the frontal lobes which control the "executive functions."
Someone explained the stealing issue this way: Our kids may have a very immature conscience and a little-kid perception of ownership: "If it is just sitting there, it doesn't BELONG to anybody, and is free for the taking." They might slip into this mode of thinking even when they have mouthed the values and rules to you previously. They don't always connect the object with the owner of the object.
Some kids with FAS disorders are compulsive about stealing. Yes, this is brain dysfunction, and while it is wise to apply consequences and hold them accountable, we need to be reasonable about our expectations.
My daughter has a problem with stealing, it is neurological, she really can't control it, so I make sure that everyone understands it is THEIR responsibility to keep money (and food in her case) out of her reach and/or eyesight. When she lived at home, this meant I had my purse in my bedroom, and an alarm on her bedroom door so I would know if she got up at night, and there is always close supervision at all times. She is never left in the house alone. She had this problem when she was 10 and she still has this problem at age 26. It's not a matter of "trust," because she doesn't have the CAPABILITY to control the impulse to take what she thinks she needs. She is a sweet girl who would never intentially hurt anyone, but she needs to be protected from her own disability. I make sure everyone knows about her problems so that we can all work together to protect her from harm (getting arrested, getting someone angry, getting punishment that won't "teach" her anything for something she really couldn't help in the first place).
I have to work with my embarrassment, but I explain to people that this is part of the disorder, she can't help it, I can't change it, so let's work together to help her. Let's do what we can to provide an environment where she won't be set up to fail. Success is spelled SCREAMS - note that the last S stands for Supervision. She needs an external brain, that would be you, the teacher, the respite sitter, whoever is available to think for her when she can't make good decisions for herself. Key word: CAN'T - not able to. Brain damage. Physical disability. Frontal lobes don't work consistenly or efficiently. We have to remind everyone of that, so she is not blamed for behavior that is beyond her control. What is within my control is providing the supervision she needs.