Correction Appended

SEEMINGLY every Hollywood studio and production company coveted “Mamma Mia!,” the international musical that had been planting Abba’s infectious songs inside theatergoers’ craniums since 1999. But Judy Craymer, the musical’s global producer, had rebuffed all advances — even Tom Hanks’s.

On the eve of the show’s Los Angeles premiere five years ago, Gary Goetzman, Mr. Hanks’s partner in the production company Playtone, met with Ms. Craymer at the Peninsula hotel in Beverly Hills. Mr. Hanks’s star power wasn’t enough, though: Playtone received the same polite no as all the rest.

So the people at Playtone applied the full extent of their trademark charm. Mr. Hanks called Ms. Craymer to convey his personal interest in the project. Rita Wilson, his wife, sent her a note gushing about the production the couple had seen in London. Mr. Goetzman, the sort of Hollywood dude who’s partial to calling everyone he meets dude, kept in touch too, even paying a visit to her home in London last fall. All along, the message was low-key but clear: In Playtone’s hands the movie would be faithful to the campy, winking stage show, and the members of the main creative team behind the original would be full partners.

It wasn’t until last year that Ms. Craymer said she felt ready to go ahead with a movie, and by that time she had come to regard the folks at Playtone — who had since produced “My Big Fat Greek Wedding” — as friends. And uncommonly resourceful friends, at that: during his visit to her home, Mr. Goetzman arranged for Harrod’s to deliver her drink of choice (Champagne, Dom Perignon in this case) and his favored Belvedere vodka. When they failed to arrive, he rushed to the store — which had already closed for the night — and sweet-talked the security guards into letting him inside to find his parcel.