Create a new world in survival. Any difficulty setting will do. Take some damage (we tried falling and drowning damage, but don't think it matters how). With less than perfect health,quit and reload the game. You will have full health when we expected you'd have the same health you had when you quit.

It does not matter if you quit to title, quit to title, close MCPE and reopen it, or quit and force quit MCPE. Some times you will see your health briefly (1/4 second at most) at the level where it left off then get replenished to full.

Confirmed on:
Samsung Galaxy S4 with Android 5.0.1
Galaxy Tab 3 7.0 with Android 4.4.2