You show a rather deliberate and determined fundamental lack of understanding of the British political system; a system which is one of the most successful and stable in the world, copied to a lesser or greater extent by many democracies on this planet.
In the UK we do not directly elect our PMs. We elect an MP for our constituency - in a free and fair electoral process. That MP 99.999% of the time is part of a political party. The party or parties who can command a majority in the House of Commons forms a government. That party's leader, freely chosen by its members, becomes PM.
To put it bluntly, Teresa May is PM because she is the elected leader of a party who garnered 11,334,576 votes at the last General Election, almost 2,000,000 more than the next biggest party. That's where she gets her mandate.