What I did when moving from transmission to deluge:
-Get the .torrent file for that torrent.
-Open that torrent, make sure it starts paused!, and point it to the directory where your existing files are. Or if you want you can move the folder somewhere else, but that can cause other issues!
-Right click the torrent and choose force re-check.
-See how many % are complete, make sure it is what you had before (ex: 48%)
-If so, then you can right click the torrent and choose resume and it will continue.