You're right, 512MB SODIMMs don't exist.
Just because you can physically put it in there, does NOT mean it's going to work. Kinda like Petrol (Gasoline) in a diesel car. You can do it, but you aint going anywhere with it.
I deal with this ALL THE TIME in work... as in this is something I try at least weekly, on both Desktop and laptop's, at the insistence of the customer. It's their money, so I do it.
2GB of ram is not going to work on anything other than a handful of laptops from that era. Consumer grade hardware will not handle a 512MB SODIMM.
also, remove your sarcasm please. I am perfectly aware that 512MB SDRAM SODIMMS exist, but they simply will not POST with the full amount of RAM recognised, if it boots at all. Hence why I never posted anything about tthem not existing. I merely wanted you to avoid buying what would likely be an expensive paperweight. If you do have one of the handful of laptops that will handle it, then well done, and good luck to you.