If a Muslim finds a dead body of a stranger in the sea, how should they proceed with the funeral? How can they decide if the stranger is a Muslim or not?

I don't know. I think in such situations the authorities in your country should be notified first. Then they will try to find out who it is and the cause of death. That can help in determining the identity and religion of the person and then the findings will determine whether there should be a funeral prayer or not.[1]

Reference:

[1] http://islamqa.info/en/2313