Just had this happen in my league. MR Renyel Pinto on the DL, fully recovered but one more week to sit before DL time expires. At the trade deadline I was able to package him in a trade to Philly for a backup outfielder. Everything seemed fine. The next day I checked the Philly box score to see how the other player in the trade performed and saw Pinto threw an inning in relief.

He still had a week of DL time when I traded him. Does the DL status not transfer from team to team?