You might try putting the parboiled potatoes on a cookie sheet with a bit of space between each potato. Place in freezer. After they are frozen, put them into large freezer bags or use a "sealing" machine if you have one, to take the air out of bag. I've done this with raw tomatoes with pretty good success.
I have never had good luck freezing a cooked potato. The water forms ice crystals in the cell of the potato and busts the cell wall. When you defrost you get a lot of water and a lump of starch. Even mashed potatoes loose a lot of water when thawed and the texture is strange. I have tried to use a mixer to put everything back together but it doesn't taste the same.
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Freezing Uncooked Potatoes