Can Shen be used as a reaction to play into a free battlefield that another player is going to conquer?

Ruling: No, Shen cannot be played to a free battlefield that another player is conquering because you don't control that battlefield at the start of the showdown.

Nuances:

• Shen's card text specifies "to a battlefield you control"
• Units can only be played to locations you control unless a card effect grants special permission (like Rengar does)
• Shen does not grant special permission to play to uncontrolled locations