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Alan Bates, who worked as a sub-postmaster at a post office in Llandudno, is portrayed by Toby Jones in the show.
He spent 20 years campaigning for people to hear the truth about what happened and even took the Post Office to court.
The Virgin founder watched the four-part drama and like many viewers was touched by Mr Bates' story.
He reached out to Mr Bates after seeing his interview in The Times where he said: "If Richard Branson is reading this, I'd love a holiday."
During ITV's This Morning, hosts Craig Doyle and Josie Gibson read out a message from the billionaire to the couple.
"Dear Alan, I did get a chance to read your moving interview in The Times, and we’d love to offer you and Suzanne a well-earned holiday on Necker Island," he wrote.
"I can’t think of anyone who deserves a break more. Hopefully, see you there. Best, Richard."
The Post Office scandal was one of the biggest miscarriages of justice in British history.
Since 1999, more than 700 sub-postmasters were wrongly prosecuted for theft, false accounting, and fraud, because of a faulty accounting software called Horizon.
It wasn't until 2019 that the Post Office acknowledged the problems with the Horizon system and prosecutions began to be overturned.
A public inquiry into the scandal began in 2021, but it is still ongoing.
Mr Bates and his wife Suzanne will also be treated to upper-class return flights, as well as a Mediterranean cruise this summer.
Fighting back tears, Mr Bates said: "Thank you very much, Richard! Much appreciated! Much needed, but very much appreciated."
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