If I play Grim Apothecary to a battlefield, can I move a friendly unit from another battlefield to owner's hand?

Yes, you can. According to the card text of Grim Apothecary, its ability states: "When you play me, you may return a friendly unit at a battlefield to its owner's hand."

Because the ability does not restrict the target unit to the same battlefield where you played Grim Apothecary, you are permitted to choose a friendly unit located at any other battlefield you control.