You can find this mission at the Sonar Collections Dock when playing as Michael, and after purchasing the dock by any of the three characters. The only purpose of this mission is to begin the Submarine Parts hunt.
You need to find 30 Submarine Parts for Abigail.
Abigail - All Submarine Piece Locations:
Once you have collected all 30, Bring the submarine parts back to Abigail.
You will be given the choice to Kill her or not.
Abigail drives an Asea, one of the rarest cars in the game. If you want it wait until Abigail gets in the car and then kill her by shooting her through the window. You will then be able to take it to a garage.
GTA 5 Walkthrough: Abigail Missions - How to get the Asea: