This short story starts with a young woman being hit by a car owned by a billionaire. She is unconscious with a head injury so he calls a doctor to meet them at his penthouse because it's faster than taking her to the hospital. When she gains consciousness she has lost her memory (doesn't know who she is or where she lives) so he lets her stay with him. She's with him for about a month and she still hasn't regained her memory but they have fallen for each other.
If You Love Me is a very quick read with an unusual story line. I didn't know that this was a 3 part novel when I started it so it looks like you really should read all three parts to get the complete story.