There may/should be some threaded holes in the clutch assembly on the same side as the fingers. Since this is a kit there may be some bolts already in those holes, maybe painted red, that are holding the clutch in the released position. If not, you may be able to thread some bolts into the holes and pull them down until the inner disk will indeed move.
The alignment tool should have two sets of splines. you insert the alignment tool in as far as it will go so that it will align both clutch disks and install the clutch.
BEFORE you remove the compression screws used for installation, the ones you inserted or the ones it came with, make sure the clutch is installed on the flywheel and all bolts are tight ... then remove the temporary bolts. Using this method will keep both disks in proper alignment while the pressure from the clutch is restored to the installed kit.
Your should now be ready to put the tractor back together.
BTW - I just did this today with a MF 240 and it worked just fine.