This should go without saying, but these days it doesn't: Ido Haar's globe-straddling crowd-pleaser of a doc, Presenting Princess Shaw, showcases real footage of the key moments of the story that it's telling. That's a joy and a thrill. When its subject's life changes, and she discovers that the art she has devoted herself to is suddenly reaching thousands, soon to be millions, we actually see her, stunned and tearful in a city square, her phone and her mind both blowing up. The thunderbolt that strikes her is a YouTube video from the Israeli mashup master Kutiman, who crafts bracing new compositions from scraps of music he excises from the postings of amateur musicians. For years, as she toiled away at a New Orleans assisted-living facility, Samantha “Princess Shaw” Montgomery uploaded clips of herself singing, a cappella, the impassioned songs she composes. She had reached only a small audience, but it included Kutiman, who set her somber, sultry ballad “Give It Up” to a groove that loops a 6-year-old's piano improvisation, a trio of drum-technique demonstrations and choice noodlings from a bass player, a pair of guitarists, a trombonist and more. None of these collaborators knew Kutiman, Princess Shaw or even that they were collaborators.

The filmmakers knew, though. And the audiences cheering through Presenting Princess Shaw get tipped off from the start: We're watching Shaw, at first, on the cusp of a peculiar sort of stardom that she doesn't see coming. Her songs, confessions and affirmations, recorded on a cellphone, might seem offhand, but they have stirring expressive power and an out-of-time beauty even before lavished with Kutiman's production. They draw on soul, hip-hop and American Songbook jazz singing, and it's a laugh in the movie when she's surprised that a cousin points out “Give It Up” sounds a little like Amy Winehouse.

Shaw's also a warm and boisterous presence, a gabby striver who keeps pushing at open mics and the YouTube game despite what seems to be the world's indifference. Before Kutiman's mashup hits, Haar overemphasizes how, careerwise, Shaw's not getting anywhere, chronicling bus trips and car problems and the drudgery of her day job. Then Presenting Princess Shaw will cut back to Kutiman in his kibbutz as he layers tracks over her singing, a distant fairy godfather about to bring her fame. The film at times edges toward something like a big-hearted prank: How long will the filmmakers let her go on believing she's not about to break through?

It's a mistake, I think, that the movie never addresses the fact that a camera crew is following her around. We see her struggling, but it's hard not to wonder, in those moments, what she makes of the attention the documentarians are giving her — and what exactly they've told her they're documenting. In a story about an artist finding the will to persevere, it's vital to know what signs have kept her keeping on. More engaging are scenes of Shaw connecting with relatives she hasn't seen in years. They discuss, with courageous frankness, a history of abuse that their family has long preferred to keep quiet.

The last half-hour, though, is a bliss-out, as happy a time as you’re likely to have at the movies. That video goes viral. Shaw gets invited to Tel Aviv to sing in a concert with Kutiman, who springs several more videos on her. She tours Israel and YouTubes all about it. She hugs Kutiman and everyone in his band. “This rocks ass!” she gushes again and again. Then, Internet-famous, she goes home — and back to work — to see what happens next.

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