Here is a summary of material about the connection between the pterosaur propatagium and the bird propatagium. The pterosaur propatagium developed into the bird propatagium.
"The pterosaur wing membrane is divided into three basic units. The first, called the propatagium ("first membrane"), was the forward-most part of the wing and attached between the wrist and shoulder, creating the "leading edge" during flight."
"The [bird] propatagium is variably deployed, relative to elbow extension, in flight; support for its cambered shape is maintained by multilayered collagenous and elastic tissue networks suspended between leading edge and dorsal antebrachium."
The elbow is set back from the leading edge and the bend in the arm is hidden by the Propatagium, a fold of skin inside the front part of the wing which connects to the shoulder and the wrist."
Through flight experiments with live birds and computer modeling we define the aerodynamic contributions of the propatagium in avian flight.
We conclude that the cambered propatagium is the major lift generating component of the wing proximal to the wrist.
This possibly advanced shoulder anatomy, combined with the presence of a propatagium linking the wrist to the shoulder (which fills the space in front of the flexed wing and may support the wing against drag in modern birds) and an alula or "bastard wing" may indicate that Microraptor was capable of true, powered flight.
a. A slightly arched surface, as of a road, a ship's deck, an airfoil, or a snow ski.b. The condition of having an arched surface.
Note that the word "patagium is used in two different ways.
In the flying pterosaurs, the patagium is also composed of the skin forming the surface of the wing. In these ornithodirans, the skin was extended to the tip of the elongated fourth finger of each hand.
The patagium of a pterosaur had three distinct parts:
Propatagium: the patagium present from the shoulder to the wrist
Brachiopatagium: the portion stretching from the fourth finger to the hindlimbs.
Uropatagium or cruropatagium: the anterior portion between the two hindlimbs, depending on whether it did or did not include the tail
In birds, the propatagium is the elastic fold of skin extending from the shoulder] to the carpal joint, making up the leading edge of the inner wing. Many authors use the term to describe the fold of skin between the body (behind the shoulder) and the elbow that houses the outer segments of the latissimus dorsi caudalis and triceps scapularis muscles. Similarly the fleshy pad that houses the follicles of the remiges (primary and secondary feathers) caudal to the hand and the ulna is also often referred to as a patagium. The interremigial ligament that connects the bases all the primary and secondary feathers as it passes from the tip of the hand to the elbow is thought to represent the caudal edge of the ancestral form of this patagium.https://bio.unc.edu/files/2011/04/FeducciaCzerkas2015.pdf
The importance of a propatagium to the evolution of the avian wing is significant, as it has no apparent function other than contributing to the aerodynamics of the animal. Therefore, its presence in flightless forms lends support to the neoflightless hypothesis (Olshevsky 1992; Paul 2002; Feduccia 2012). The discovery of a propatagium in members of all clades of core maniraptorans, including Caudipteryx (oviraptorosaurs), Microraptor (dromaeosaurs), Anchiornis (a putative troodontid; Chatterjee and Templin 2012), Archaeopteryx (a basal urvogel; Martin and Lim 2005), and the basal avian Scansoriopteryx (Czerkas and Feduccia 2014), is additional evidence that flight was basal in Aves. Similarly, four-winged tetrapteryx wings can best be interpreted in a flight context.