If a player during the season transfers from one team to another:
1. Go to the tab Teams, open the the previous team, go to its roster, find the player, click Edit
The new pop-up window will appear, add the End date (date when player is released from this team). Click Save
The end date appears in the roster. Player is released from this team.
2. Now open the the new team, go to its roster, add this player in the new team's roster with correct Start date.
3. If the respective team takes part in more than one competition during the same season, player should be released from all of them.
If your league uses functionality of the Clubs in FO, the same procedure with the adding of the End date of the player in the previous club should be done. Also the player with correct Start date should be added to the new club.