2. Question: According to the opinion brought in the Magen Avraham (Orach Chaim 637) who says one is allowed to steal from a non-Jew but it is not considered yours, meaning the non-Jew still owns it, why would a lost object of a non-Jew which we poskin a Jew is allowed to keep be any different since the Divrei Chaim and Gilyon Maharsha both say the lost object of a non-Jew is considered ownerless even before he gives up on it. Why is the lost object of a non-Jew owned by the Jew if he finds and takes it but if a Jew steals from a non-Jew even if it is permissible why does it still belong to the non-Jew (as long as he does not give up on it)?
A. One small hint, but why does it make for a difference: When the non-Jew’s object got into the hands of the Jew by the lost object the non-Jew didn’t have it but when it got into the hands of Jew when stealing it was in the hands of the non-Jew.
Answer: Because the object was in the non-Jew’s hands that gives him ownership and keeps it with him even after it is stolen since he had control over the object but the lost object, the non-Jew has no control over the object therefore there is nothing to link ownership to him.