In any case, it didn't belong to the Ottomans to give away.

Getting it as gift from a conquering entity, does not make any of it better.

I mean, if you really want to go down this way, it does not really belong to the Egyptians either. It's not because current-day Egyptians share the same land as antiquity Egyptians that they are the same people – countless waves of war, massacres, migrations, emigrations happened in the last 4 millenia.

By that logic who does it belong to? How long does someone need to be in an area to be the "owner" of it. The people on Egypt currently weren't there when it was moved. Why should they get it? The people that were there when it was moved definitely weren't there 3000 years ago when it was made. Did they own it? In fact who owns anything in the world?

easy, never give away or sell ancient artifacts. Would you be fine with people conquering rome, and selling it all stone by stone? Would you be OK with some Italian dictator doing it?

Rings true to me. The notion of ownership has been extended to almost everything and it makes no sense that anyone can claim ownership of an ancient obelisk. Or rather, we should distinguish between "I'm the caretaker of", "I'm the one who benefits from", and "I can do whatever I want with".