Well I wish it were that simple.
The problem is that when partner B bought out partner A, that closed the business as a partnership, and partner B (the surviving partner) starts a new company as a sole proprietor. That also means a final partnership income tax return, closing the company sales tax registration, etc etc
The purchase agreement would post to the partner A equity drawing account, thus zeroing out the partner A equity and to a partner B liability account. With the partnership closed the liability of the installment loan become a personal liability.