The Sophie's Choice actress reached out to the makers of the 2008 film after she saw the stage production, which features the Swedish band's songs, and the personal note she sent them helped her snatch the part of Donna Carmichael from Kidman.
Ulvaeus tells Britain's Daily Express that the Moulin Rouge! star was in the running for the lead, but adds, "Then we received a handwritten letter from Meryl Streep saying how much she had enjoyed the show and we realised that was the age group we should be casting from. And she said yes straight away and that was the 'open sesame' (beginning moment) for everything."
The Hollywood version of Mamma Mia! proved a huge hit at the box office, raking in more than $609 million (£380 million) globally.