Is it permissible to deduct amounts added by the third partner as fictitious expenses without his knowledge, given that the other two partners bear these false expenses and that the partners' accounts are collectively managed by one of them?

If the third partner is doing what was mentioned, then the questioner and his partner must prevent him and demand that he bear the imaginary expenses, and remind him of the Qudsi Hadith: "Allah says: 'I am the third of two partners as long as one of them does not betray his companion. If he betrays him, I depart from between them.'" If he refuses and they are unable to extract their right through legal means, then deducting the amounts without his knowledge is a matter of scholarly disagreement. This is the issue of al-Zafar, and the preponderant opinion on it is explained in Fatwa No. 45630.