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Who is Thomas Thabane?
Mr Thabane, 80, is one of Africa’s oldest leaders and has spent most of his working life as a politician.
No stranger to political rivalry, Mr Thabane once fled to South Africa, alleging a coup plot by the military and had to be escorted back to Lesotho by the police.
Why hasn’t he been formally charged?
In the February court case his lawyer argued that his position as prime minister granted him immunity from prosecution.
The case was referred to the High Court. But the High Court has not heard the case yet.
It is not clear why the case has taken so long to come to court.
Mr Thabane insists that the accusations against him are politically motivated.
Why has it taken so long for him to resign?
It may be that he was trying to negotiate with his party to get an agreement that the investigation would be dropped in return for him resigning.
If that is the case, it hasn’t worked so far.
A spokesperson for Mr Thabane’s party, the All Basotho Convention (ABC), told the BBC’s Pumza Fihlani that it will not be supporting any attempt by him to get immunity.
He has resisted immense pressure from his own party to resign earlier.
Around the time of his court appearance he announced that he would not step down until July.
He cited old age as the reason for his resignation, without mentioning the murder case.
In April, South African mediators negotiated a deal which promised a “dignified” exit.
But a few days later he was reported to have said that he will not be pushed out of office until he is ready to leave and that nobody had the right to set the time for his departure.
What next for Lesotho?
The current finance minister, Moeketsi Majoro, looks set to be the prime minister. He has been appointed as the would-be leader of the new governing coalition by both the ABC and its ally, the DC (Democratic Congress).
The king of Lesotho – a tiny kingdom completely surrounded by South Africa – is being formally notified and it is expected that Mr Majoro will be sworn in at the royal palace in the capital, Maseru, on Wednesday.
Parliament will then reconvene on Friday, when the new government is expected to be inaugurated