Probably a bit better than your phone, depending on models (phone, extender, router), of course. At least in theory repeaters can have better antennas and more power to spare.

If you can put a network cable though at least one of the walls you might as well just put an outdoor AP (main building) or WiFi bridge (shed) there. That way the signals only have to go through one wall.

You can put your phone in hotspot mode and place it where the extender should go, then see how good the signal in the office is.

I think it will partially depend on the model of extender you bought.