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(The grease is a good idea. In fact they come factory greased. If you see no grease in yours it is because it is dryed out and that is one add on to the problem. If your sponge is too dryed out, it canot be saved. In fact the sponge will split once you slice it. It will just crack. The grease keeps the sponge from drying out and cracking. The grease also helps the tension to be smooth and keeps the sliding from jerking or hanging up. Therefore you put grease throughout the foam.
The foam as a whole does not move on the rod but stays in the housing/cradle. Just where the rubber goes is where the sliding happens; of course.
Also if the cap somewhat does not seem to snap back in place tightly. Don't worry about that part. The cap will stay put by the weight of the tub.

I will also make a video how to fix the struts on front load washing machines.....look for it..