If a unit starts on battlefield B, gets charmed to battlefield A during the opponent's turn, then is moved back to battlefield B via Ride the Wind before combat resolves, does the controlling player conquer battlefield B?

Ruling: Yes, you conquer battlefield B when your unit moves back. What matters is whether you have already scored that battlefield this turn, which you generally would not have during your opponent's turn.

Sequence:

• Unit starts on battlefield B at the start of opponent's turn
• Opponent charms the unit to battlefield A
• Before combat resolves, use Ride the Wind (an action) to move the unit back to battlefield B
• You conquer battlefield B and score a point

Nuances:

• If you had already conquered battlefield B earlier during the opponent's turn, you would not conquer it again (no point, no conquer effects trigger)
• The presence of enemy units on either battlefield does not prevent the conquer from happening