The Rama (Rav Moshe Isserles of Cracow, 1525-1572) writes (Orah Haim 276) that if a person needs to walk to a dark place on Friday night, after Shabbat has begun, he may ask a non-Jew to bring a lamp and hold it in that place. Although one may not benefit from a light kindled by a non-Jew for a Jew on Shabbat, it is permissible to ask a non-Jew to bring a lamp that was already lit.
The Taz (Rav David Halevi Segal, Poland, 1586-1667) infers from this ruling that it is permissible on Shabbat to ask a non-Jew to move an item that is considered Mukseh. The Rama permits asking a non-Jew on Shabbat to bring a lamp, which is Mukseh, seemingly proving that one may ask a non-Jew to move Mukseh items on Shabbat.
The Magen Abraham (Rav Abraham Gombiner, Poland, 1637-1682) and the Elya Rabba (Rav Eliyahu Shapiro of Prague, 1660-1712) disagree. They claim that the Rama’s ruling applies only in that particular case of the lamp, since even the Jew is allowed to move the lamp in a certain way ("Tiltul Min Ha’sad" – indirectly moving something), and the light is needed for a specific purpose on Shabbat. According to these Poskim, one cannot apply the Rama’s lenient ruling to all situations of Mukseh.
As for the final Halacha, Hacham Ovadia Yosef ruled that one may ask a non-Jew to move a Mukseh item in the specific case of a "Keli She’melachto Le’issur" – a utensil normally used for an activity that is forbidden on Shabbat, such as a pen or other writing utensil. Halacha permits moving such an object on Shabbat if he needs it for a permissible purpose – such as if one wants to use a pen to scratch himself – or if he needs the space it currently occupies. One may not, however, move such an item to protect it. For example, if one sees his pen outside on the porch and is afraid it may be stolen or ruined, he may not bring in inside. However, Hacham Ovadia rules that in such a case one may ask a non-Jew to bring in the item, just as the Rama permits asking a non-Jew to bring a kindled lamp on Shabbat. Since it is permissible to move the item under certain circumstances, one may ask a non-Jew to move it when it is forbidden to move it oneself. When it comes to other Mukseh items, however, one may not ask a non-Jew to move the item on Shabbat.
Summary: A utensil that is generally used for an activity that is forbidden on Shabbat – such as a pen – may be moved on Shabbat only if one wishes to use it for a permissible purpose, or if he needs the space. One may not move it to protect it from getting ruined or stolen, though one may ask a non-Jew to move such an item for this purpose.