The Duchess of Sussex reportedly wrote the letter after the Oprah interview in March 2021.
The portrait was taken during His Majesty's 70th birthday and showed a happy family.
The Duchess of Sussex also called His Majesty "very charming" in the "Harry & Meghan" Netflix docuseries.
The Duke and Duchess of Sussex wed at St. George's Chapel at Windsor Castle on May 19, 2018.
The Duchess of Sussex will remain in California to celebrate her son Prince Archie's fourth birthday on May 6.
Prince Harry will attend King Charles III's coronation while the duchess will stay with their children in California.
The Duchess of Sussex has successfully trademarked her website with a logo featuring a handwritten "Tig" with a full stop at the end.
The Duke of Sussex admitted that he is no longer on speaking terms with Prince William and King Charles III.
The Duke and Duchess of Sussex remain undecided on whether they will attend the ceremony or not.
"Don't cry about not being invited to weddings. You chose to leave, now go and live it – and be it," the duchess said.
Lawyers say the couple's number of working hours is "not unusual" given they are directors at their foundation.
The Duke and Duchess of Sussex have received an invite but have yet to confirm their attendance at the ceremony.
The Sussexes have only until after King Charles III's coronation on May 6 to stay at the cottage.
The Sussexes' children received their HRH titles when King Charles III became the new monarch in September 2022.
The Sussexes raised serious claims against the Firm in their Oprah Winfrey interview and in their "Harry & Meghan" docuseries.
Britain's Prince Harry has accused Buckingham Palace in court documents of withholding information from him about phone-hacking and said he was exposing the alleged wrongdoing by tabloid "criminals" out of love for his country.
Britain's Prince Harry arrived at London's High Court on Monday for a hearing against the publisher of the Daily Mail newspaper over alleged phone-tapping and other breaches of privacy.
The Duke of Sussex is in a legal battle with the government over a decision not to allow him to personally fund his police protection while in the country.
The Sussexes have yet to announce their decision if they will attend the ceremony or not.
Prince Harry will on Friday seek to win his libel claim against publisher Associated Newspapers without the case going to trial, his lawyer said, as the British royal steps up his legal battles against the tabloid press.
Buckingham Palace changed Archie and Lilibet's titles from Master and Miss to HRH Prince and HRH Princess.
A representative for the Sussexes confirmed they have been invited to the coronation on May 6.
