As far as I'm aware a "transfer controls" option does not exist. If it does I'll be happy to implement what's needed to the aircraft. However from what I understand this is not possible, neither do gauges fully function in the second pilot seat.
EDIT: Okay I looked it up in the MDS and there is this option, it must be enabled in the mission file though. You will find me with the same name (F22-Raptor-2006). I will need someone else in hyperlobby with version 4.1 to test this... They also need to be capable of hosting the mission.
P.S. Use of control transferral demands much more network traffic.
EDIT 2: Tried in multiplayer. I believe there are some bugs with the current MDS code and control transfer. Yet to test it with control transfer off, but with control transfer on. It is possible to hijack the controls, without the guy in the main pilot seat giving you the controls. When he gives you the controls your joystick is still disabled because you are a crew member. So you must use keyboard. Keyboard strokes only work for 1 second, after that you must press the key again etc... Joystick is disabled the whole time no matter what, as long as you are a crew member it is disabled. Based on this theory, it would be possible for any crew member to take control of your plane by simply using the keyboard controls when they jump into your plane... regardless of whether control transfer is enabled.