"A" and "B" were partners in a business as per an agreement that suggests to divide the profit and loss equally between them after deducting a portion of their sponsor under whose commercial registration the business was running. Meanwhile "A" desired to withdraw from the business, because he wanted to increase the portion of the sponsor according to the valium of the profit realized, which was rejected by "B". "B" had wanted to hide the increasing of the profit from the sponsor. So "A" declared that he had withdrawn from the business. But "B" denied to give "A" his entitlements in full. Only a part of the same was given to "A". The remaining was withheld with him justifying that there was a court case against the sponsor regarding some financial commitment in which if he would file their business firm would be liable to pay for him. When the matter was disputed both agreed to appoint an arbitrator and accept his verdict whatever it may be. "A" gave "B" the choice to nominate the arbitrator eventually he accepted the person appointed by "B". Finally the arbitrator issued his verdict fixing QR 2000 for "B" considering him as a working partner and to divide the profit and loss equally between them considering "A" as a silent partner. Also he suggested to increase the portion of the sponsor. Accordingly "B" paid "A" some amount from his arrears in two installments. But after 3 months he denied to pay the balance to "A", saying that he doesn't accept the verdict of the arbitrator. After five years when "B" decided to go for Hajj he approached A with an offer of 15 thousand riyals. Then A told him if he wanted to clear himself from his financial liabilities it should be on the basis of the related account. According to the accounts checked by the arbitrator there was more than 40 thousand riyals to be paid to "A" at the date of the arbitrator's rule. However A went for Hajj paying nothing to A even the amount offered by him.
Is the stand taken by B right according to Shariah? In the event of appointing an arbitrator, would it legally be binding up on the concerned parties? Would A not be considered as a continued partner entitling the profit for following period of the verdict given by the arbitrator in addition to his previous arrears?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

What we understood from the question is that the matter is one of the two circumstances:

First, if the arbitrator dissolved the partnership of the two partners, so dissolving it as it is stated in the question is correct and both of them are bound to execute the verdict as that was concluded by the arbitrator with their consent provided his ruling corresponds to the truth. 

It is incumbent on partner 'B' thereupon to pay his partner 'A' what he agreed to be bound with according to the verdict of the arbitrator, as he was pleased with it.  The Prophet said: "The Muslims must fulfill their conditions." [Al-Bukhari]

The Prophet also said: "When people differ, they come to me, and I judge between them. Both of the parties are pleased with the ruling, and this is a splendid thing!" [Abu Daawood]

On the above grounds, the partner 'A' is entitled to 40,000 QR only, and this is what the arbitrator ruled.  If partner 'B' delayed in paying back the money because of being in hardship, then there is no harm on him.  But if he is well-off and procrastinates then he is sinful. However, partner 'A' is only entitled to the mentioned amount, because it is a debt, and debts are to be paid back at exactly the same amount. Adding an extra amount to this original amount is Riba (interest and/or usury).

Secondly, if the arbitrator approved the partnership, but determined that for it to exist, partner 'B' should pay his debt to partner 'A'.  Therefore, it is an obligation on partner 'B' to repay his debts, and partner 'A' should not ask partner 'B' to pay interest on that amount (debt) because debts have to be paid back in exactly the same amount. Partner 'A' is also entitled to the benefits of the company according to his share.

Allaah Knows best.