The idea that birds are descended from pterosaurs has an interesting history. The idea was proposed by Harry Govier Seeley. But note the negative reaction he received. Not much has changed in that respect.
Seeley was also an authority of pterosaurs, and in 1901 published a popular book on the subject, Dragons of the Air. In it, he gave an overview of animal flight, reptiles, the discovery of pterosaurs and pterosaur skeletal structure. He initially believed that birds descended from pterosaurs, but under intense criticism from his peers, backed off this assertion and argued that they shared common ancestry. "It would therefore appear from the vital community of structures with Birds, that Pterodactyles and Birds are two parallel groups, which may be regarded as ancient divergent forks of the same branch of animal life," he wrote.
His popular book on Pterosaurs, Dragons of the Air (1901) found that birds and pterosaurs are closely parallel. His belief that they had a common origin has been proved, for both are archosaurs, just not as close as he thought.
I suggest that pterosaurs and birds are as close as Seeley thought.
Ornithodesmus (meaning "bird link") is a genus of small, deinonychosaurian dinosaur from the Isle of Wight in England, dating to about 125 million years ago. The name was originally assigned [by Harry Govier Seeley] to a bird-like sacrum (a series of vertebrae fused to the hip bones), initially believed to come from a pterosaur. More complete pterosaur remains were later assigned to Ornithodesmus, until recently a detailed analysis determined that the original specimen in fact came from a small theropod, specifically a dromaeosaur. All pterosaurian material previously assigned to this genus has been renamed Istiodactylus.
By the 1840s, however, there was little doubt that Cuvier had been correct, and some naturalists were very impressed by resemblances between the skeletons of the flying fiends [pterosaurs] and birds. As Richard Owen stated in an 1874 monograph of Mesozoic fossil reptiles:Every bone in the Bird was antecedently present in the framework of the Pterodactyle; the resemblance of that portion directly subservient to flight is closer in the naked one to that in the feathered flier than it is to the forelimb of the terrestrial or aquatic reptile.Just like Owen, Seeley saw no way to “evolve an ostrich out of an Iguanodon,” but Huxley turned the argument from convergence against his opponents. The traits supposedly shared between birds and pterosaurs had to do with flight, and given that both lineages had become adapted to flying, common traits in their skeletons were to be expected. The diagnostic traits in the hips, legs, and feet of dinosaurs, on the other hand,were found in all birds, not just ground-dwelling ones. This meant that these characters marked a true family relationship and not just a shared way of life.