So, you are telling us that the prop slides on the prop shaft? The only way it could do that is if the drive (shear) pin is a loose fit in the prop or prop shaft or both. Pop the rubber cover off the end of the prop for a looksee. Probably a badly worn pin or wrong pin.
OR..if the shaft is sliding in and out of the gearcase, that is a different matter. Some movement is normal, a eighth of an inch is suspicious. Several things can cause that, including missing thrust washers, badly worn front thrust bearing, worn spline ends on shaft. You would have to go in for a look.