Whose intention is considered valid when someone else performs the washing upon another person?

Primary text

The intention of the person being purified is what is considered, not the intention of the person washing them. This is because the person being purified is the one addressed regarding the obligation of ablution, and the ablution is achieved for them. The washer, conversely, is merely a means and is not directly addressed by the obligation, nor is the ablution achieved for them, similar to a vessel or one carrying water.