Should Bilbo have given the ring back to Golloum?

[The Wizard from Milan]

Should Bilbo have given the ring back to Golloum?

If somebody founds something, he/she is not the proprietor of the thing. He/she should give it back in exchange for a percentage compensation. Do you agree? Does this rule apply here?

It looks like the rule is over-ruled by the fact that Bilbo becomes aware of the fact that Gollums intends to murder him before he becomes aware of the fact that Gollum is the proprietor of the ring. Do you agree?

Or is the goverining rule the fact that Smeagol did not get possesion of the ring in a legitimate way and that the descendants of the ligitimate proprietor are untraceable?

By the way, who is the legitimate proprietor? Deagol and his heirs? or Isildur and his heirs? Or is it Sauron?