As per Atticus' answer, the ball was not on the green, so no relief because of the puddle on the line of play. You say winter rules were in operation, so lifting the ball was ok, but it was put back in the wrong spot, so was played from a wrong place - which equals a two shot penalty.
But ... the score only stands (including the penalty shots) provided the player had not gained a significant advantage by playing from the wrong place. I'd suggest that playing from a spot where the puddle didn't intervene on the line did gain the player a significant advantage. So he should have replayed the shots from the right place using a second ball and then reported it to the committee for adjudication. I suspect the OPs partner/FC didn't, so probably should be disqualified?
