Sry for reviving this thread, but I recognized something interesting when using the above mentioned method.
The original screenshot on my PS4 had a size of
443 kB (picture 1). The screen I have sent with a PS message and saved it afterwards on my tablet with the playstation app has a size
3 times as big (1380 kB, picture 2). But as you can see, there seems to be zero quality difference. Probably a bug within the PS-messaging system or the android app?
Picture 1: Original file, imported via USB
Picture 2: File saved via PS-App