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Setting the stage, my opponent uses Akodo Zentaro to steal my Imperial Storehouse, and places it in his province next to his dynasty deck. I then trigger Governer's Spy, and turn all his dynasty cards facedown.
What happens to my Imperial Storehouse? Does it stay facedown in his province? Does it discard? Does it immediately transport itself to the province next to my dynasty deck?
If the card does not go facedown into his province, how does the rest of Governor's Spy resolve? My opponent will have 3 cards in his provinces, and the spy says that each province needs to end up with at least one card. Do I do "as much as I can", placing the 3, and then the 4th refills once the action finishes, or am I unable to fulfil the effect and it fizzles?

A faceup holding is considered to be “in play” and thus the act of turning it facedown would cause it to leave play. Therefore, it would return to the appropriate out-of-play area controlled by its owner instead of staying in the Lion player’s province, and thus it would be placed in one of the Scorpion player’s provinces.
When rearranging the facedown cards, the controller of the Governor’s Spy would get to decide which card goes into which province. Because the Imperial Storehouse cannot be put into any of the Lion player’s provinces, it would instead move to the equivalent province among the Scorpion player’s row—for example, if you attempted to put the storehouse into the Lion player’s leftmost province, it would instead be placed in the Scorpion player’s leftmost province (remember that orientation is mirrored). After fully resolving the ability, the Lion player’s empty province would be refilled.

[Tyler Parrott, Sep 16 2020]