And so too do Transport Secretary Chris Grayling, Business Secretary Greg Clark and Commons Leader Andrea Leadsom, despite widespread speculation that Mrs May would demote them.
Meanwhile, Britain's Northern Ireland Minister, James Brokenshire, has resigned ahead of a planned cabinet reshuffle.
May's Cabinet reshuffle was more limited than expected with the big names all keeping their jobs, including the gaffe-prone Boris Johnson keeping his position as Foreign Secretary, the newly promoted Defence Secretary Gavin Williamson staying on and Philip Hammond hanging on as Chancellor of the Exchequer after his Autumn Statement, or budget, was received well by Tory MPs.
Reports suggest that around half a dozen of her senior ministers could be axed or moved, with Number 10 sources indicating the more junior ministerial appointments would continue into a second day on Tuesday. The BBC had been reporting at the time that Grayling would be named party chairman but the report and the tweet, were both wrong.
David Lidington was appointed as minister for the cabinet office, replacing May's closest friend in parliament, Damian Green, who was forced to resign previous year over misleading statements over pornography found on his computer.More news: Rivals Texas A&M reporter Courtney Roland goes missing in Houston area
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His replacement was announced on Twitter, only for the tweet to be nearly immediately deleted.
Mr Lewis will also take on the role of minister without portfolio.
Sir Patrick McLoughlin, a minister as far back as the Thatcher government, could be replaced having overseen the general election campaign that ended with the Tories losing their majority.
Foreign Secretary Boris Johnson, a leading Brexit supporter, is expected to keep his job despite challenging May's strategy a year ago. Damian Green was the third minister to leave the cabinet in the space of a few weeks, after the defence secretary and global development minister both quit - all three following separate scandals.
He was also blamed for the disastrous party conference, where magnetic letters fell off during May's speech which was being televised live.