It may actually work as Layth describes if the stat increase from Morale happens before ilevelsync take effect.

If Morale applies before ilevelsync then the the Hellwolf Choker of Aiming would be Morale boosted from +12 Det +12 Crit to +13 Det +13 Crit and then synced down to +10 Det +13 Crit as the i80 stat caps for jewelry are +10 Det/Pie +14 All others.

Ilevel isn't a stat budget in XIV, but a gear stat cap determiner. Pretty much all Green and Blue gear have a "Main" Secondary stat which is at the ilevel stat cap and a "Secondary" Secondary stat which is at roughly 2/3 the ilevel stat cap.