What is the ruling on the *mahr* when the husband delegates the option of divorce to the wife, and she chooses separation?

Primary text

If the husband grants her the option and she chooses separation, or if he appoints her agent to pronounce divorce and she does so, it is treated as if it were his own divorce, and her *mahr* is not forfeited. This is because although the wife physically enacts the divorce, she is acting as his deputy and agent, and the action of the agent is treated as the action of the principal, as if it originated from his direct action.