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Coincidentally, both Ms Adams (46) and Ms Richardson were members of Parliament for Selwyn when they were appointed to the finance roles.
Both were also law graduates from the University of Canterbury and both married farmers.
Ms Adams replaces Steven Joyce, who announced this week he was leaving Parliament.
Ms Adams and Mr Joyce stood against Simon Bridges to become National Party leader.
Ms Adams would have taken over the finance role regardless of whether Mr Joyce remained in Parliament.
Ms Richardson remains in the minds of many political observers for carrying on the legacy of former Labour finance minister Sir Roger Douglas.
She and then National social welfare spokeswoman Jenny Shipley combined to make the most significant changes to social welfare seen since the system was introduced.
Dame Jenny later went on to become prime minister.
Ms Richardson eventually got offside with former prime minister Jim Bolger, leaving Parliament to follow a boardroom career.
Ms Adams yesterday signalled a strong focus on ensuring the continued success of the New Zealand economy.
She says she will fight hard against Government policies slowing New Zealand down.
Like Ms Richardson, Ms Adams wants to advance new economic and social policies ahead of the next election.
''But first we have to stop the threat posed by Labour's economic mismanagement.''
Many of the Labour-led Government's planned changes would sacrifice New Zealand's economic success and make it harder for New Zealand businesses to compete and succeed, Ms Adams said.
Slower business growth meant less investment, fewer job opportunities and lower wages generally than would otherwise be the case.
Crown financial figures released yesterday showed an improvement in the Government's accounts for the seven months ended January, with a higher tax take indicating more people in work.
However, Ms Adams singled out Labour's overseas investment changes, employment law changes and proposed new taxes as things which could hurt New Zealand's medium-term economic performance.
Ms Adams' first major task will be holding Finance Minister Grant Robertson to account after he presents his first Budget on May 17.