family member can't make purchases with shared payment method

From: How to share purchases with your family - How to share purchases with your family - Apple Support

"When you turn on purchase sharing, everyone in your family gets access to apps, music, movies, TV shows, and books that family members buy. The family organizer is billed for family members' purchases."

The second sentence is incomplete because others can still pay for their own items, they just have to use personal account balance to do so (see the tiny footnote near the bottom of the page). This dies not include that person's other payment methods such as shared Apple Pay. It can only be the organizer's method or the person's individual Apple balance. Turning on purchase sharing simply activates the feature whereby if a family member does not have adequate personal balance to pay for something then the organizer's payment method (e.g., credit card) will be charged.

Read the document for the link to "learn how purchases are billed if a family member has Apple ID balance". This tells you how it works.

The payment method for Family Sharing is automatic:

1. If anybody in the family buys or subscribes to something, Apple first attempts to charge the item to that individual's Apple Account (Apple ID) balance, if any.

2. If a family member does not have enough personal Apple Account balance, any excess will be charged to the Family Organizer's primary payment method (usually a card of some kind). The Organizer's personal balance will not be used for purchases made by other family members. If it cannot bill the primary payment method, the Organizer will need to make another payment method the primary method.

- "Some purchases, including gifts, can't be billed to Apple ID balance and will be charged to the family organizer's payment method." "Some subscriptions might not be charged to Apple ID balance."

Ref:

- Family purchases and payments - How to share purchases with your family - Apple Support

- How apps, content, and subscriptions from Apple are billed - How apps, content, and subscriptions from Apple are billed - Apple Support

- Check your Apple ID balance - Check your Apple Account balance - Apple Support

- Change, add, or remove Apple ID payment methods - Change, add, or remove Apple ID payment methods - Apple Support

Adding funds to your Apple ID balance:

- https://support.apple.com/HT203021

- How to redeem your Apple Gift Card or App Store & iTunes gift card - Apple Support

- Add money to your Apple Account balance - Apple Support

Partly because I had to guess what you meant by shared payment method and the lack of any details that would allow me to determine the problem. I therefore presented the only two methods Apple will let you use and hoped that you could figure out the problem from there. The only aspect of sharing involved in Apple's methods is the Organizer will share their payment method with other family members unless the other members have personal Apple ID balance. If you're asking something else then you need to explain what you mean by shared payment method, but essentially what I wrote before covers all the payment methods available. Simply saying you can't do something without providing additional information doesn't allow us to be specific in our solutions we offer. Quoting a specific error message or describing exactly what you are trying to do and at what point it fails would help determine the issue. If it is a problem with the organizer's payment method, see:

If your payment method is declined in the App Store or iTunes Store - Apple Support

Change, add, or remove Apple ID payment methods - Apple Support