What is the ruling on a deficient amount of money, and must it be repaid, knowing that I was entrusted with it and preserved it just as I preserve my personal money and travel documents?

If you safeguarded the money your manager entrusted to you without negligence or dereliction, until you delivered it exactly as you received it, then you are not liable from a religious perspective, as the Prophet (peace be upon him) said: "There is no liability upon one who is entrusted." Liability becomes obligatory if there was negligence on your part in safeguarding the trust. Any dispute should be resolved by the judiciary or by scholars.