Is the entire amount deducted from the purchase price as a result of negotiation efforts permissible for one partner, or must the other party share in it?

Partnership is based on agency, and each partner is an agent for the other in the company's affairs. An agent is a trustee (amin), and the nature of trusteeship dictates returning the deducted amount to the company's funds, because your partner has a right in it. It is not permissible for you to exclusively take anything from the company's funds without your partner.