Is it permissible for someone whose belongings were taken by mistake to take similar belongings of the one who made the mistake, knowing it was a mistake but without identifying the exact person who made it?

It appears there is no legal impediment for a person to take an item from someone who mistakenly took his item due to its similarity, because the first taker benefited from the item he took, so the second person has the right to benefit from his item in return. It is preferable that neither of them use the other's item unless they have despaired of finding their own.