First of all, it’s worth noting that you can only get the FIB Emergency SUV in Grand Theft Auto 5 during the Hotel Assassination mission when you will play as Franklin.
The getting the SUV part is pretty easy: when you get in front of the hotel, instead of finding a good shooting point for your assassination mission, run straight forward to the entrance of the hotel and you will find the vehicle parked there. Simply get inside and drive like a pro.
The mission will instantly fail, but don’t choose to restart the mission. Instead, quit it and you will be spawned right next to the FIB SUV with no police around. Make sure to drive it all the way to your garage to save it. You’ll have a really nice collection soon!