The agency will help the organisation with its comms and develop awareness and behaviour change campaigns around money management and debt.
Third City will use comms to help people take action before their finances become unmanageable and to understand the link between financial planning and positive outcomes.
Graz Belli, Third City founding partner, said: "Tackling financial capability remains a major challenge for the nation… our campaign will centre on advocacy and peer-to-peer comms to shift social norms around money and the behavioural traits influencing how people manage their finances."
The service's creation in 2011, following the rebrand of the Consumer Financial Education Body, was handled by Fishburn.
The account win comes as the agency announced that it was promoting Chris Blackwood, PRWeek UK’s 2012 ‘Young PR Professional of the Year’, to full partner.
Blackwood, who takes up his position today (Tuesday), was described by PRWeek judges as being part of a "new breed of super-numerate PR professionals".
The agency said Blackwood would lead on developing its measurement and analytics capabilities.
Mark Lowe, Third City co-founder, said: "Chris has the skill-set that every forward-thinking agency is looking for. I’m just glad that we found him first."