Moving a project into Ableton or Logic

Hey guys, I can’t figure out how to move the tracks 1-4 into another recording program while preserving the place they are on the OP
For example, I individually moved tracks one through for from disk mode and dragged them into Ableton, but they all pushed to the beginning of the track, is there a way to move a project easily from the OP to Ableton while preserving the place they were on the machine?

turn off auto warping in Live’s preferences.