They will need to purchase the membership product to be marked as a member, but that can still be done.
What will happen, is you will create an order for the customer, and you can discount the membership product so that they do not have to pay for it again. You can even put in the order notes once it is created why it was discounted and reference the order number where they did pay for it earlier.
The next piece, would be to adjust their renewal date.
- Go to Reports->Sales->Memberships
- This is a list of all your members. You can click on the table header that says Name to sort the whole list by name
- Find the customer you need to update.
- In the Next Charge column, adjust this to the correct date that this customer will have to renew their membership