I would suggest checking the episode where he is in the hatch alone injecting himself with syrum... Maybe the picture is set up there...

And to shoot down the idea that he brought it back ( ie the time travel idea ) he woke up in the forrest. now if he brought things back... he would have had his clothes from the bar, and the picure and shoes... maybe eve red ones... j/k but he was naked and he found the picture at the Hatch. That means it was in the hatch to begin with. he probably had it with him on the boat...