Any instructions by the deceased are not binding on the estate and do not supersede any will that they may have left. Clubs have gotten into trouble by paying a beneficiary when the proceeds should have gone to the people named in the will. So the first step is to check with the executor of the estate, and get written permission to pay the beneficiary.

Secondly, any instructions by the deceased do not supersede the Partnership Agreement of the Club. In other words, a dying member can not choose a new member for the entire club. There should be agreement among the remaining members to accept this new member.

If an inheritor is already a part of the club, or if they want to join the club (and the club is OK with this), there are some steps the club can use to reflect the step up in basis that the inheritor would receive:

Enter a withdrawal for the deceased member in the accounting system as normal, *except* that when choosing the account, select Suspense. If you do not have a Suspense account listed, you can use any account, just make sure to note the amount of the withdrawal.
Complete the withdrawal, and the Suspense account will be negative, but do not pay out any money.
The day after the withdrawal, enter a payment for the member(s) joining the club, in the amount of the withdrawal. Enter the payment into the Suspense (or whichever account was used), and the member will have ownership of the units at the stepped-up basis.
Keep in mind, this is intended to be used only for someone who would be legally entitled to receive the value of the deceased's club position.

Please Note that a withdrawal report will still be generated in this case. However as long as this is being done to step-up the basis for someone who is inheriting the member's units in the club, any capital gain from taking the withdrawal can be ignored for tax purposes.