I am arch mage and i can't start the quest. I noticed that somehow i allready have grand staff of charming in my storage (not quest item).

You can try the following:

If the staff is found before starting the quest, it will have weight, and can not be removed from the player's inventory. The quest will not show an icon on the map and dialogue options are not available to return the staff to Enthir. To fix these issues, equip the staff, and activate a weapon rack. An icon will then appear, hinting to pick up the staff. Picking up the staff will update the quest journal, directing you to return the staff to Enthir.

http://www.uesp.net/wiki/Skyrim:Onmund%27s_Request

P.S. If you haven't started the quest at all you can try talking to Onmund. If the dialog does not appear, leave the cell where he is then go back and talk to him again it may appear.