Is it permissible for a partner in a project to take his due from his partner who falsely claims losses, and to do so without the latter's knowledge?

The jurists have agreed that a partner is an أمين (trustee) over the company's assets, and thus is not liable except in cases of transgression or negligence. His claim of loss or damage is to be accepted with his oath. If his claim of loss is not accepted, you may demand an oath from him, or refer the matter to the Sharia court.