I don't think he could tell him to putt as he is further away! Player B could just say no, you're up!
On The Green - Page 2
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I wouldn't have thought this would be allowed, but it would be one response when he refuses to move the marker:
Ball-Marker Pressed Down by Opponent
Q.In a match, the player's ball-marker on the putting green is pressed down by the opponent. Is the opponent in breach of the Rules?
A.No. Rule 18-3b does not apply to ball-markers. However, if the ball-marker were moved such that it no longer accurately marked the position of the ball, in equity (Rule 1-4), the opponent would incur a penalty of one stroke. If the opponent pressed down the ball-marker with the authority of the player and that act caused it to move, there would be no penalty to either player (see Decision 20-1/6).
I could see the marker being ruled a moveable obstruction and if your opponent didn't move it, you could. It would be your opponent's responsibility to make sure the ball gets replaced properly or he would incur a two stroke penalty, so it's in his best interest that he mark his own ball. If I had to move the mark, you would bet I'd be looking to make sure it got replaced on the exact blade of grass upon which it was previously resting.
As noted, the etiquette rule could be invoked with disqualification possibly resulting.
So much for a gentlemen's game.