Qyburn's ability allows you it take control of a non army character in your opponents dead pile. If my opponent chooses SER Preston Greenfield (TK), then activates SER Preston's ability to send him back to shadows which shadows does he go to mine or my oppenent's.

My friend and I think he would go to my shadows because I am the owner of the card but we just wanted to check.

As you say, when a card leaves play for any reason, it goes to the corresponding out-of-play area belonging to its OWNER, no matter who controls it when it leaves play. Taking control of Greenfield, then sending him to Shadows will indeed send him to his owner's Shadow area, and give control back to his owner.