Bring the butter and puffball puree to room temperature, then process in a food processor until smooth and combined. Transfer the mixture to a mixing bowl and stir in the salt, lemon zest, juice, and parsley. Form the butter into a 1 inch log, wrapping in plastic wrap, then label, date, and refrigerate until needed. The butter can also be frozen.
After you make the puree above, you can use it to make things like this. The puffball butter is a concentrate, so it needs to be cut with something, in this case a little more butter for a variation on classic Maitre'd butter. It's excellent on steaks, of course.