It's difficult to save a replay in a multiplayer game, because you may have only very limited time before the game continues to the next hole.
Best thing is to hurry to the "save" window and just copy the URL to your buffer. You may then store it in a text file for replay, or post it on your wall.
My usual practice (in solo games) is to send the replay to my own email address - this overcomes the 10 slot limitation of the profile.
Another caveat: Replays in the profile list cease when you delete them - no use to save their URL.