When installing the marathon on a plane, you follow the instructions for a lap belt installation (there is no latch on the plane). They probably should read through those instructions prior to using it on the plane. What I do when installing the seat on the plane is put the carseat on the airline seat. Recline the airline seat. Put the lap belt through the belt guides on the carseat and then buckle the seatbelt. Tighten the buckle by pulling the strap. Return the airline seat to a full upright position (remember I put it in recline to install the seat).
When buckling the seatbelt, make sure that the lever release on the seatbelt is facing down (this will mean you have to turn it over from how it typically would be if you were buckling it on yourself). When the seatbelt is tightened on the britax seats, the buckle release lies really close the carseat shell. When it gets time to get the carseat off the plane, if the buckle release is too tight against the carseat shell, it is really hard to get it unbuckled. By flipping the buckle upside down, the release is easy to get to so you can unbuckle the carseat easily.
If you have a seatbelt extender (that seatbelt piece the flight attendants use to demonstrate the seatbelt during their safety speech), this helps get that buckle portion out of the belt path on the marathon, so if your friend can get that piece, it should solve most problems. If they can't get it, make sure they flip the buckle as I mentioned in the previous paragraph.