Board Game Arena

I am about to do the last move in my game with no time limit. Will I be able to view it after it ends, after some time? If so, then where? I have already played some correspondence games and I cant find them. I am not a premium member if it matters

Go to your user menu (click your avatar in the upper right corner of any BGA screen).
Click your name/avatar. This will bring up your profile.
Either click the part of the banner that says XXX Games Played to display just the list, or scroll down to see the list of completed games (most recently completed shown first).
Clicking any game name will bring you to the summary screen for that game (final score, statistics). At the top of that page will be a button to show a replay of the game. [Note: There have been some short periods in BGA's history from which replays are not available.] These replays can be done from any player's perspective, so you can see the information they saw.

This applies to all players, premium or not. It actually allows anyone to replay any game, so they can effectively sit behind a master level player and try to understand the strategy behind the decisions.