How can one atone for the sin of stealing money from the wallet of an unknown Christian person? Is it permissible to give the amount in charity on his behalf, and will this benefit him even though he is not a Muslim? If it will not benefit him, then how can his right be restored?

The disbeliever benefits from his good deeds in this world, and his punishment in the hereafter may be lightened because of them. So, if you owe a debt to a deceased Christian and cannot find his heirs, it is permissible to give the amount as charity on his behalf. This will benefit him in this world, and it may lighten his punishment in the hereafter, as Ibn Baz said. This does not contradict the fact that the deeds of disbelievers are scattered dust, for the intent is that they will not enter Paradise nor escape Hellfire. However, their punishment may be lightened due to their good deeds. Al-Qurtubi said: "The lightening [of punishment] is specific to those for whom a text has been revealed."