It must be the ultimate piece of sporting memorabilia for the son of a world leader.
Michelle Obama raised eyebrows with her gift of model helicopters for Gordon and Sarah Brown's sons during the Prime Minister's recent visit to Washington. For yesterday's return visit, the First Lady gave five-year-old John Brown a little piece of US history: a black full-size Louisville Slugger baseball bat a marked with the presidential seal and signed by her husband.
The slugger is the official bat of major league baseball in the United States and has a pedigree dating back to 1884.
She also gave John a book of classic baseball photos by Walter Iooss Jr, while the Browns' younger son Fraser, two, was given a set of the classic American children's books by Dr Seuss.
Mrs Obama was equally generous with the Queen, presenting her with an engraved iPod. It was unclear whether there were any music tracks for the octogenarian head of state, but the device did contain footage of the Queen's 2007 visit to America.
Mrs Brown, who gave the Obamas' daughters clothes from TopShop during her trip to the White House, gave Mrs Obama T-shirts, jeans and miniskirts for her children from Marks & Spencer's Autograph range.
Yesterday Mrs Obama visited one of Mrs Brown's favourite causes at Charing Cross Hospital, where she met cancer sufferers and their families in the Maggie's Centre to mark its first anniversary. The First Lady hugged Maysie and Presley Cogdell, who were there with their mother Trudi, 44, who is on her third course of chemotherapy to treat the breast cancer which has spread to her bone and liver.
"She was a very lovely person, very friendly and very interested in what goes on at Maggie's," said Mrs Cogdell, from Hammersmith, west London. "She had a long talk with Maysie. She told her the Vice President had a granddaughter called Maisy and she loved the name." Maysie gave Mrs Obama an Easter card decorated with the Union Jack and the Stars and Stripes.
Namina Turay, 32, told the President's wife that she had been diagnosed with breast cancer in 2007, but had now been in remission for a year. "Congratulations on being done!" the First Lady replied, telling her to "keep it up".
The spouses of the G20 leaders were later entertained to dinner at 11 Downing Street. Guests included the Harry Potter author JK Rowling, the child psychologist Dr Tanya Byron, the supermodel Naomi Campbell and the dot.com entrepreneur Martha Lane Fox.
David and Samantha Cameron gave their own gifts: a £250 Lara Bohinc bracelet for Mrs Obama and, for her children, a copy of The Railway Children and a book of Shakespeare stories.
The President gave Mrs Cameron a bracelet by David Yurman and books for their children, The Wonderful Wizard of Oz pop-up book and a copy of Hans Christian Andersen's Fairy Tales.
Today, Mrs Obama and the G20 spouses will visit the Royal Opera House for a programme of operatic and ballet extracts. JK Rowling will give a reading during the performance, introduced by the broadcaster Mariella Frostrup.
G20 fashion: First Lady chic
While Sarah Brown sported a sober black outfit that suggested she had heeded the Metropolitan Police's advice to dress down, the new US first lady's take on G20 chic was a cardigan covered in silver beads and sequins which showed that the Obama roadshow has lost none of its sparkle.
Michelle Obama has an ability to pull off the kind of daring bright colours that even former supermodel Carla Bruni rarely attempts, and her pistachio green skirt was in a particularly springlike shade that suggested a fresh era in world politics. Rather than wear an expensive designer label that might have been seen to embody the consumer excesses against which the protestors were railing, the first lady of fashion had chosen the decidedly non-elitist high street chain J.Crew. Not only is J.Crew affordable, it is also American, and Vogue cover girl Obama is known for her support of homegrown labels – on Tuesday she boarded Air Force One in a pearl tweed coat by Thakoon and stepped off it in a belted chartreuse silk dress by Jason Wu, the label of the asymmetric white gown she wore for the inaugural balls.
It's possible she spent the flight rifling through alternatives, but Mrs Obama manages to look comfortable and spontaneous whatever she wears. One trick she uses to avoid looking overly prim – a trap most first ladies have plummeted into – is to slightly mismatch her jewellery. And, unlike Sarah Brown, who wore thick black tights to reflect the gloomy issues of the summit, Michelle Obama's legs were characteristically bare. After all, a chilly economic climate doesn't faze a true fashion leader.