We were lucky in that the teen was under 18 when she graduated from HS and was still under 18 when she left for college. We set up a bank account for her and deposited her checks into it until they stopped, but she knew that once they stopped, so did any money outside of what we wanted to give her.
She got a job and worked and saved money through half of HS and all of college.
If she had turned 18 and was still in high school, we would have had her sign the check and then made it disappear into the family budget. She knew where it was spent already, she knew what the costs of food, power, car insurance and repairs, gasoline, and extras cost before she got to the point of having to do it ALL herself. I sent her shopping for food all the time and she had to live with what she bought for all of us and our complaints when she didn't shop well. She was able to admit it wasn't easy and that I knew what I was doing when it came to spending and paying bills.
We always reported $0 saved.