The "Welcome to Manhattan" Power Core and Charge puzzle in Control Resonant explained

The puzzle to Move the Charge to Central Checkpoint between Power Cores in Control Resonant as part of the early "Welcome to Manhattan" quest is probably the first confusing bit of the game that most players will encounter. Here the goal is to get an electrical charge by hitting it with your weapon, and bring it from one power core to another at the Central Checkpoint and power it up. Problem is, the charge doesn't last long enough for the journey to said Checkpoint, dissipating and forcing you