What is the ruling on partnering in trade with a disbeliever or a transgressor? And is Zakat obligatory on the capital remaining with the partner if it will be paid in cash, or by converting it into the cost of constructing a building for rent, knowing that the partner may not pay Zakat or may pay it to impermissible recipients?

A Muslim's partnership with a disbeliever or a transgressor in trade or work is permissible, just as the Prophet, peace and blessings be upon him, did with the Jews of Khaybar. This partnership is prohibited if it leads to showing allegiance to or loving the disbeliever, or if the disbeliever will exclusively manage the company. Rather, the Muslim must oversee the transactions to ensure that no usurious or prohibited dealings occur.

Sheikh Ibn Baz stated that the default ruling for a Muslim's partnership with a disbeliever in trade is permissibility, provided that it does not lead to showing allegiance, committing a forbidden act, or neglecting an obligation, and that the Muslim supervises the work.

Despite the permissibility, it is better for a Muslim to partner with Muslims to safeguard their faith and wealth. As for your withdrawal from the company and your share remaining as a debt owed by your partner, this means your relationship with the company is severed, and you owe no zakat (definition) on its assets. However, you do owe zakat on the debt your partner owes you, and the details of its zakat depend on your partner's situation: whether they are wealthy and willing to pay, or insolvent and procrastinating.