It can be a little bit tricky to complete. The reason for that is that the side quest Mean Dogs will interfere with the completion of this quest. Here is the proper way to trigger and complete these:

Complete the side quest Handyman’s Assistant part 1 and part 2, as well as An Explosive Plan before even approaching Bob and thus starting Mean Dogs. When you go to see the Kennel Master next to the Recruitment Office, you can pick up the fifth item for Handyman’s Assistant Part 2, and Part 3 for Handyman’s Assistant, thus completing those before talking to Bob. Complete the main quests First Steps in Prison, The Mole Queen, A Diversion, Water for the Trip, and Weapons for the Battle. This will start the main quest The Great Escape, where you can go to Jey and start the escape. You can now ask “Problem? You don’t look so good.” which will start this side quest.

Jey mentions an Abundance guard who stole his trinket. The guard in question is the Abundance army sergeant standing with his dog outside the Recruitment Office. If the events of Mean Dogs have played out where his dog attacked him, you can no longer talk to him.

After his refusal to give up the Lucky Charm try to reach an arrangement. Turns out the sergeant is looking to feast his eyes on something other than the Technomancer’s apprentice, which will trigger another side quest; Another Face. When you complete Another Face, return to Jey with the trinket who turns out to be a picture of his wife to complete The Lucky Charm.