I was finally able to get a VIDEO of this issue.
I must apologize twice over for the quality of the video. First because it was filmed while in the car and also for my very quick and rough attempts to blur out my text message numbers/content.
The video shows how I received 2 text messages when my phone was off, one from Android and one from iPhone. When turned on, the iPhone shows both texts on the lock screen, but then when unlocked, ONLY the iPhone message ever appears in the Messages app and the Android sent text message disappears and is gone forever.