Does freeing a slave on behalf of someone with their prior order fulfill the required expiation when compensation (*'Iwad*) is stipulated?

Primary text

If a person frees a slave on behalf of another with the latter's explicit command and stipulates compensation for the emancipator, the manumission is valid for the beneficiary and fulfills their *Kaffarah*. The *Walaa* also belongs to the beneficiary. This is the view held without known dispute by Abu Hanifa, Malik, Al-Shafi'i, and others, based on the principle that the manumission occurred using the beneficiary's money, analogous to purchasing a slave and appointing the seller to free them on the buyer's behalf.