Use saved fallheight to determine a character's jump state.

The jump state initial state is "none", and it is set after physics simulation.
If a save is done just above the ground, the character may land before
the first run of the simulation, effectively cancelling the effect of
falling.

CHANGELOG.md

@@ -86,6 +86,7 @@
     Bug #5703: OpenMW-CS menu system crashing on XFCE
     Bug #5706: AI sequences stop looping after the saved game is reloaded
     Bug #5731: Editor: skirts are invisible on characters
+    Bug #5739: Saving and loading the save a second or two before hitting the ground doesn't count fall damage
     Bug #5758: Paralyzed actors behavior is inconsistent with vanilla
     Bug #5762: Movement solver is insufficiently robust
     Feature #390: 3rd person look "over the shoulder"

apps/openmw/mwmechanics/character.cpp

@@ -883,7 +883,11 @@ CharacterController::CharacterController(const MWWorld::Ptr &ptr, MWRender::Anim
         }
 
         if(!cls.getCreatureStats(mPtr).isDead())
+        {
             mIdleState = CharState_Idle;
+            if (cls.getCreatureStats(mPtr).getFallHeight() > 0)
+                mJumpState = JumpState_InAir;
+        }
         else
         {
             const MWMechanics::CreatureStats& cStats = mPtr.getClass().getCreatureStats(mPtr);