To start this mission you should talk to Guillaume DeGarmo whom you will find in the Terrabrew Cofee. He will ask you for help in making the exchange. You will receive from him and Old-Earth Plate meant for exchange.
Gem Jealousy
Related points of interest
Objectives of Gem Jealousy
1. Make the exchange with George Saint-George
Guillaume asked me to get his gem back from George Saint-George. Hopefully this plate is enough for George to make the exchange.
Go to Terrabrew Coffee in Commercial District and talk to George Saint-George. He will be very happy to trade in gem for the plate you brought. He will also explain to you what kind of relationship he has with Guillaume DeGarmo.
2. Return to Guillaume
I have the gem. I should return to Guillaume.
To complete this mission, return to Guillaume DeGarmo and inform him that you have recovered his valuable item. You will receive 100 XP and 1800 credits for doing so.
I've made the exchange and got Guillaume his prized gem back. Hopefully he takes better care of it from now on.