>> 1. Some items are from areas now controlled by very different people to those for whom the item was originally important. Do modern descendants of the Spanish have any moral claim to Aztec or Inca artefacts, for example?
> 1. Most Mexicans or Peruvians have indigenous ancestry, they are not exclusively (or even mostly) descendants of the Spanish. It would be better to return those artifacts to the descendants of those from whom it was stolen.
This is an "easy to say, near-impossible to do" task that's been shoved with little effort from the proposer onto the museum staff. Short of comprehensive DNA analysis, finding the proper descendants for a particular artifact is not trivial. The response given does not take into account multiple competing claims towards the artifact, nor the possibility of all descendants that could properly claim it being dead, whether natural or not.
>> 2. Some items have complex histories, where multiple competing countries could all claim it as part of their history. Where the item was found is not the end of the story. Items from Greece, Turkey, Cyprus for example.
> 2. Who has an even weaker claim than all other claimants? The British Museum.
Calling misdirection on this response: It does not properly address the original question posed.
In an attempt to give a proper solution: Items with histories from multiple countries will have to put it into a round-robin-style sharing agreement, where the item/artifact will pass through the countries one by one before circling back.