Can Your Adult Child Contribute to a Health Savings Account?
Even if your son is on your family's insurance policy, he may be eligible to contribute to a HSA.

Question: My son is 22 and works full-time, but he’s still covered by our family health insurance policy. Can he contribute to a health savings account? - M.B., Woodstock, Conn.
Answer: As long as he is covered by a high-deductible, HSA-eligible health insurance policy and can’t be claimed as a dependent on anyone’s tax return, he can contribute to an HSA. And because he’s covered by your family policy, a loophole in the law lets him contribute up to $6,900 to the plan in 2018. You and a spouse can also contribute up to a combined $6,900 plus up to $1,000 each if you’re 55 or older.