I recommend keeping copies of all correspondence with airlines when reporting the loss. Read your insurance T&C very carefully. Make diary notes of phone calls to airlines where there may be no paperwork. Keep receipts for all "emergency" purchases.

Insurance companies are good a taking your money and even better at finding ways of avoiding giving it back.

Needless to say, at least you are with a major airline and language may not be the barrier that it could be in other parts of the world.