All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
In principle, a proxy is a trustworthy person, and shouldn`t guarantee-whatever he is entrusted with-except in case of misconduct or negligence.
Al-Imam Ash-Shirbini said: "A proxy-even with Ji`alah (conditional payment)-is entrusted with whatever he receives and spends from the wealth of the authorizer, and he is required to guarantee that wealth in case of misconduct or negligence, just like similar persons." {Al-Iqna` Fi Hal Alfaz Abi Shojaa`, 2/321}.
Moreover, the person entrusted with delivering funds is required to protect them against loss, theft and the like, so keeping funds in an unsuitable place of custody is an act of negligence on his part. Hence, a car isn`t a suitable place for keeping money; therefore, if the proxy has left or forgotten that sum in his car, and it was stolen, then he is considered negligent and guarantee is required from him.
In conclusion, the above proxy is required to guarantee the Zakat funds- referred to in the above question-from his own money, and distribute them among the eligible recipients, and without telling his sister (authorizer) about what has really happened. And Allah knows best.