If a unit takes damage during combat on one battlefield, then moves to another battlefield to start a new showdown, does it heal from the first combat before the second showdown starts?

Question

Accepted Answer

Ruling: Yes, the unit heals from damage taken in the first combat before the second showdown begins.

Sequence:

The combat showdown on battlefield 2 must fully resolve first, even if you no longer control units there
After battlefield 2's combat ends, damage on your unit heals
Then the new combat showdown on battlefield 1 begins with the healed unit