Essentially, my world has arthropod-like creatures with exoskeletons based on chitin, but while some are mostly like earth arthropods, one group specifically developed traits more observed in vertebrates, such as a jaw that opens vertically and structures slightly similar to lungs with air sacks, quickly diversifying into niches more commonly filled by vertebrates. However, I'd like at least one species of said vertebrate-like arthropods to be capable of flying similarly to pterosaurs, and by that I also mean having their wing structure and intricate membrane or patagium (which was made of skin, muscle, blood vessels and special fibers called actinofibrils, which helped stiffening the membrane in certain areas and minimize unwanted flapping), in something like the following sketch:
My main problem however is that powered flight only truly evolved about four times as far as we know, and all instances of limbs adapting into membranous wings belong to vertebrates, with arthropods having developed in a way that, as far as we know, didn't involve any limbs whatsoever and certainly don't rely into membranes to fly. Thanks to that, I'm struggling to find out whether something like the wings of a pterosaur could be replicated by a creature with an exoskeleton rather than an endoskeleton and skin.
These creatures would ideally grow to be about a meter long, weighting roughly 8-10 kg and with a wingspan of roughly 2 meters. Their planet is similar to planet earth during the carboniferous period. They live mostly in open regions devoid of tall obstacles where vegetation doesn't hinder their flight. Their nymph stage is flightless and aquatic, with their wings only appearing at adulthood after they undergo a pupa-like stage, but I planned for them to live for a period of time of up to a few decades after reaching adulthood.
With that in mind, is there any way that a creature with an exoskeleton could specialize its limbs and part of its exoskeleton into functional pterosaur-like wings? My main concern is whether a membrane made of soft chitin (like observed in arthropod joints and the exoskeletons of some caterpillars and other larvae) layered with muscles would be able to work well enough or if I would need to essentially give them something akin to skin along with their exoskeleton.