From Archon Arcana - The KeyForge Wiki
Captured Æmber is taken from an opponent’s Æmber pool and placed on a creature controlled by the capturing player. Players may not spend captured Æmber.
When a creature with Æmber on it leaves play, the Æmber is placed in the opponent’s Æmber pool.
Unless otherwise specified, Æmber is placed on the creature that captured it.
—KeyForge Master Rulebook v17 April 2023