Yes. First you'll need to locate the saved game file you want to transfer.
Second, you'll need a tool that is able to upload files to the inside of an application sandbox on your iPad. Two possible tools are iFunBox for Windows or iExplorer for the Mac.
Open the FTL app in your iOS file explorer. Browse to the FTL app and you will see a file structure that includes a
Library/Application Support directory with a
prof.sav file. This is the default save file, but if you have enabled Game Center, there will be a separate
prof.sav file under each player ID inside the
players folder here. Make a backup copy of the files here, if you wish to be on the safe side. It would also be a good idea to kill the FTL app on your iPad if it is currently open, to prevent the game from overwriting your changes when you save and quit. (double-press your home key and swipe it away on iOS 7, or press the
X on iOS 6)
prof.sav file on your local PC. You will notice that there is a separate
ae_prof.sav file alongside it, which contains all your progress ever since you installed the Advanced Edition patch.
Last, copy the
ae_prof.sav file to the iPad, under the same folder where you find the
prof.sav. (if you have multiple gamer profiles, you will need to be careful; it's difficult to match up Game Center IDs except by trial and error, so be sure to make a backup if you are concerned) Then delete the
prof.sav on the iPad and rename
prof.sav. (since the iPad version only has Advanced Edition content, there was no need for a migration from
(Note: if you have not yet played the Advanced Edition on the PC, but you want to play AE on the iPad, you can just transfer the