The second map part is an item found during Dragon Slayer. It is one of three pieces of the Crandor map needed to travel to Crandor island.
The second map part is sealed in a door without a keyhole in the Dwarven Mines under Falador. This door and room is located east of the mining shop that sells bars and ores. To open the door to this room, the player will need a lobster pot or crayfish cage, a silk, an unfired bowl (soft clay molded into a bowl but not hardened by fire), and a wizard's mind bomb. With these items, the player will be given access to enter the door and in that room, there is a chest which contains the second map part.
This is a piece of map that you found in a secret chest in the Dwarven Mine. You will need to join it to the other two map pieces before you can see the route to Crandor.