Correct, if KL was the operator of the last flight segment, it is their problem! However, your father will have to be able to demonstrate proof of what is missing. This is frequently the challenge! If he had photos of the gifts he was packing in his luggage, he would be much better off. If not, it's his word against the airline's. Otherwise, every flyer that checked a bag would suddenly have $10,000 in cash in their checked bag that went missing upon baggage being lost or delayed. Likely, even with a well-worded complaint, the most he'll get from KL is an apology and a token offering. Sorry that he is having to deal with this, hopefully the family will understand that this was not an issue of your father's rudeness but an airline issue beyond his control!

Good Luck!