We have a member that wants to pay his son's health insurance. The son is not on the account. With written auth can we allow this transaction post?

It is not up to you to 'allow' this to post. It is authorized by customer (member) and company. This is basic ACH Rule Book stuff...should have this on hand and review if you are accepting transactions as a receiver.

Agree with kiemo...The written authorization is between your member and the company sending the ACH.

I also agree. My account is debited on a monthly basis to pay my son's car insurance. The car is owned by him and he is not on my account. Never been a problem.

Yes, you may allow this per NACHA Operating Rules, which allows any customer to authorize a debit to their account by signing an agreement with the originator. The bank is not required to verify this agreement is in place unless the customer disputes the charge, then the bank asks for a copy of hte authorization.