Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
It is forbidden for you to deduct the money taken by your partner from the Zakah owed on you because by doing so you protect your money and use your Zakah for yourself. This is forbidden in Shari'a and the Zakah will remain due on you.
Allah knows best.