injured players on free agent list

If a team cuts an injured player and someone else takes him off the free agent list-is he still injured on the new roster?

The injured player is out the same number of games for any team. When trolling for free agents the red I will display in the free agent list beside any player that was injured when released. The red I will display the remainder of the league no matter if he has served his time or not. If you click on the player and you don't see the phrase "injured thru game X" then he is elligible to play right away. If you pick him up and put him in your lineup he will play in your next game and the red I will be removed after that night's games.