How do you keep Materia when using Chapter Select? What carriers over when swapping chapters?
Your characters' equipment and XP are "saved" at the end of each chapter. So if you want to get the MP Absorb from chapter 14 and take it back to chapter 7 with you, you have to make sure to finish chapter 14 with it. Just grabbing it and quitting back out to Chapter Select immediately isn't enough. Unfortunately my experience has been that it isn't entirely clear exactly when a chapter transition occurs; keep an eye on the main quest, which should tell you.