Recovery and Disposal of Unknown Copper Compound
Unlikely. Copper hydroxide adsorbs carbon dioxide from air rather
fast, forming basic carbonates. if you want to test, try to boil it.
Copper hydroxyde looses water under mild heating, forming black
copper oxide.

Most likely it is either basic copper carbonate or one of basic
copper sulfates or a mix of both. I highly doubt that it is a pure
copper sulfate, as Mg had to go somewhere.
If you want to be a responsible citizen (which is not actually much
a point with relatively safe copper salts), add some soda, leave
overnight and then filter off the precipitate with filter paper.
If no filter paper is present, cotton white, toilet paper, and
similar should work, just be careful to not tear them. The
precipitate then may be heated until black and disposed any way
suitable.