Your ball comes to rest on the putting green after a shot.
Then that ball moves again before you hit the next shot.
Properly handling this situation under the revised 2019 Rules of Golf depends upon:
1) whether the ball has been marked and replaced yet or not; and
2) who or what moved that ball.
PLAYER ACCIDENTALLY MOVES THE BALL ON GREEN: In the process of marking the ball or setting up to hit the next shot on the putting green, if you accidentally move the ball or its mark in some way, simply put the ball back.
This includes accidentally kicking the ball as you walk up to it, dropping the mark onto the ball, bumping the ball with your hand as you mark, touching the ball with the putter as you set up, etc.
If you accidentally do anything to move your ball as you mark it or after you mark it, just pick up the ball and put it back on its original spot; nothing else is required. (Same thing if your opponent or fellow competitor accidentally moves your ball on the green: just put it back.)
NATURAL FORCES MOVE THE BALL ON GREEN: Now, if the ball moves from that at-rest spot on the putting green because of natural forces (wind, water, slope, gravity), what happens next depends upon whether or not the ball has been marked and replaced.
If a ball on the green has been marked and replaced and then natural forces move that ball before a stroke is made, the ball must be replaced on the original spot. It doesn’t matter how far the ball rolls or where it ends up (in the hole, in a penalty area, etc.). A player should not benefit from nor be penalized for either situation, since neither was the result of a stroke. So simply put the ball back on the original spot and play on.
But if a ball moves again after coming to rest and that ball has NOT yet been marked and replaced, the ball must be played from the location where it ends up once it stops. Since the ball was not marked, this ‘natural forces’ movement is considered a continuation of the previous stroke. So in that case, simply play the ball where you now find it.