What is the ruling on partnership in purchasing real estate through Islamic Murabaha, where one partner pays a portion of his lawful money, and the other partner pays a down payment from money earned from her work in a non-Islamic bank, knowing that the first partner will cover the remaining installments from the property's rental income?

If your partner gives you a percentage of her salary, which she obtained from an interest-based bank, then it is not permissible for you to share it with her, because this salary is not hers to own, and it must be spent on charitable causes. Your sharing with her in that case would be considered cooperation in sin. However, if what she gives you is from lawful money, then there is no objection to sharing it with her.