Is it permissible for one partner to pay Zakat on behalf of another partner without his permission, and what is the ruling on partnership with him, and is it permissible for the manager of the shop to distribute Zakat without the partner's permission?

Withholding the obligatory zakat is a grave crime and a major sin, for which its perpetrator deserves condemnation in this world and punishment in the hereafter. The default for a Muslim is to be free from this sin, and it is impermissible to accuse someone of it without clear proof. If you are certain that your partner does not pay his zakat, then it is incumbent upon you to advise him and explain that zakat is an obligatory duty and a pillar of Islam, and that wealth is not diminished by charity. It is not permissible to pay the zakat on his behalf without his knowledge and intention, because zakat is an act of worship that requires the owner's intention. Dealing and partnering with someone who does not pay his zakat is permissible, but it is better for a Muslim to deal with someone who fears Allah in himself and his wealth.