Probably not, but it's easy to try:

1. Cycle your car from "off" to "on" eight times. With the final cycle landing in the “on” position.
2. You will hear the doors lock and unlock to acknowledge the car is program mode
3. Press any button on the first keyless entry remote (primary)
4. Repeat on second and any other remote you want to program (up to a total of four)
5. Turn the key off when you are done
6. Test newly programmed remotes

They're probably not even the same frequency, but you can try..

 

I highly doubt it because of the way they are programmed.

 

And the fact that the 2010 uses a key while the S550 is a true push button start. No key to put in. The 2010 lacks the communication equipment to read the key and start the car or unlock the doors.

 

The 05-14 still read the transponder in the key for PATS a the lock cylinder, the car won't
start without it. There is no lack of communications here. It also wirelessly communicates
to lock and unlock the doors. There is no lack of communication here either.

It's that the newer cars are wireless communications, you have antennas in the car that read the keyless
FOB for starting as well. However, should your FOB battery fail, there is an inductive backup in the center
console that will read the fob by powering it inductively. Also, it's actually not so keyless, there should be a
key blade inside the FOBs.

The FOB functions for locking and unlocking are programmed separately then the key, on the S197,
as the fob is separate from the key anyhow. SO, as we all said, we doubt you can program a fob
for the button functions, and not for starting it. As we said, you probably can't use it for just the
button functions because of how they are programmed, and when done, the FOB becomes fully
functional anyway. Even if the key blade inside the FOB won't work with the car, the FOB will start
the car, lock and unlock it. They need programmed at the dealer unless you have Ford-VCM.

Furthermore:
Even though you do not need a key, the key should be inside the FOB, because if the FOB battery
dies, you can't unlock the car. You can remove the cap at the door handle, and use the actual KEY
to unlock the car, then put the FOB in the center console pocket to start the car. They are required
to provide this backup method in case of fob battery failure, else you would be stranded if it happens.

My VW is push button start, but the fob still has a flip-out key blade. I have another FOB from the same
year car, different key, but I can program the FOB to the car, just the key won't work. Should the
battery fail, I have a lock cylinder at the door. Then if I press the start button with the keyfob, the
car starts with the dead battery in the FOB. There always has to be a backup so you do not get
stranded, getting IN the car, and starting it. SO, I can remove the key-blade from this FOB, and
still use it. SO, if he has another Ford FOB, it can be programmed to the car, but the key inside
the fib would be useless.