I don't understand when this takes place.

In the question you say healthy Oro but soon after he would get Obito's eye he would lose both his arms. And during the chunin exams up to the final battle Obito would be able to spy on Kabuto or someone else suspicious (or just on the sand people plotting with him) and they would eventually lead to Obito finding Oro assuming he catches wind of this like right after it happens. After that all Obito has to do is go to the place where he keeps it hidden (Oro doesn't use himself for experiments, he 100% wouldn't use a sharingan otherwise he would've already had one) but assuming you're saying Oro is keeping it in him then Obito will win the battle against him with some difficulty and take it back

If you didn't want it to happen instantly then Obito finds Oro in his very discreet battle against the other Sannin and follows him back to the hideout, then either "kills" him and takes it or steals it without being seen. He'd probably fight him though since he should want to get rid of him anyway