How to play Heroes of Might and Magic III online via Hamachi?

Conditions: two computers, two identical versions (SoD with the latest version of WOG installed - 3.58f). Using Hamachi, we managed to connect and enjoy the game. Problem: The game freezes when a computer-controlled hero attacks a player-controlled hero. The player who is being attacked sees "opponent's turn" (even though that turn has already ended). The second player, whose hero is attacking, sees the message: "wait for the battle results." We can't wait for the results - after a minute of waiting, the game crashes with an error. Has anyone encountered this? Please suggest a solution.