Air carrier First Officer reported a battery pack fire in main cabin during cruise. Pack was placed in TCB (Thermal Containment Bag) and the flight continued.

Narrative

We were in cruise from ZZZ to ZZZ1 when the purser called us to inform us there was a battery pack on fire. A child had plugged their phone into the battery pack to charge it. The battery pack experienced a thermal runaway and caught fire. The child woke up her mother and the mother notified a flight attendant. One of the FAs is previous firefighter and another passenger in the back of the aircraft was a firefighter. They put the pack in the lavatory and ran water over it initially while the thermal containment bag (TCB) was sourced. The aft FAs put the battery pack in the TCB and zipped it up; eliminating the fire and stopping the smoke from worsening. The purser was the dedicated communicator for all flight attendants to the flight deck. The purser informed us that the electrical smoke had then ceased and the remnant smoke within the cabin was dissipating. Captain and I were ready to divert to the nearest suitable airport if the condition worsened. We ran through the FOM. Since the fire was extinguished; with positive confirmation from the purser; the captain and I; with all FAs input as well; decided to continue to ZZZ1. The rest of the flight was uneventful.