What is the ruling of Sharia on a partner calculating the capital at the value of the dollar at the beginning of the year, knowing that the local currency is collapsing and the partnership is based on a percentage of the profits?

The standard for calculating capital and profits is the currency agreed upon in the contract, irrespective of its value fluctuation against the dollar or other currencies. Therefore, your uncle is not entitled to alter the calculation of capital and profits due to changes in currency value.