What should a Muslim young man do who lives in Russia and rents a house from a Christian woman, and he found a cross in the house, knowing that he does not have the right to throw it away? Is it permissible for him to hide it until the end of the rental contract?

You do not have the right to destroy or lose this cross, as it belongs to that woman, and it must be returned to her. You are not permitted to keep it in the house because it is an objectionable item that must be removed. Therefore, you must give it back to its owner or ask her to take it. There is no sin upon you if it remains temporarily until it is handed over.