If a master permits his slave to discharge expiation via money, can the slave free himself (self-manumission) for it?

Primary text

If the master permits his slave to discharge expiation through manumission (which implies self-manumission), there are two narrations. One holds that it suffices because self-manumission is a form of freeing a neck that suffices for others, thus it suffices for himself. The second narration states it does not suffice because the permission granted by the master is understood to apply only to freeing another slave. This latter view implies that if the master explicitly permits self-manumission for expiation, it is valid. If the permission is general, he cannot free himself if his value exceeds the minimum required for expiation.