This should give a big boost to your friendship with him. Then return to Gamlen's home and talk to Carver and show him the letters. After you are done with Birthright, head to the Gallows and speak to Tiberius. Family History This quest is available only if Carver is the surviving sibling, and it starts after finding Tiberius's Documents in Amell's estate cellar. If you are done with the area, agree to Carver's suggestion to leave the area. Once you loot it, head up to the vault room and get the will from one of the chests. One of them should have a key to the vault room.
Head west, killing enemies along the way. This begins a companion quest, either Family History or Portrait of the Past depending on whether Carver or Bethany is with you. In the room to the north, find a chest that contains either Tiberius's Documents or Portrait of your Mother. Head to Darktown, and there to Amell's estate cellar. Then talk to your sibling (Carver/Bethany) and agree to go search for the will. Birthright Receive this quest when you talk to your mother at Gamlen's House.