IANAL but I doubt that you could use an asset you did not own to raise a deposit. However, the will which left him 1/3 and the valuation of the property would indicate the value he is due to inherit. But maybe he has a poor history of paying loans and the banks are too risk averse to give him a mortgage based on a promise of an inheritance. After all there is no guarantee that he will use the inheritance as a deposit once he gets it into his possession.
Could you and your other sibling give him the money for the deposit as a loan, to be paid back when he uses the house value when he becomes the legal owner. You annd your other sibling might have greater trust in your sibling than the bank. And is “deposit” the wrong word, he would not be handing ownership of his 1/3 to the bank if he drew down a mortgage?
Alternatively if that is not possible for you or your sibling, the suggest selling the house and each taking your 1/3 in cash. Then your sibling can use that money as a deposit on a different property.