Does the partner in the turkey farm's profits have a share in the amount refunded by the Tax Authority, given that the tax record is in my name?

If the taxes are paid from the profit of the period your partner worked with you, then he has a share in what was returned to you from the value of the invoices, because you are partners in it, and it does not matter that the tax register is documented in your name. However, if you are asked to pay a tax for the period he worked with you, then you have the right to demand from him what is due from what was taken from you.