No, that's the opposite of how it works, and that's what I'm saying in my comment.

The original owner doesn't lose valid title just because it was stolen, and two people can't hold valid title at the same time (unless shared obviously, but you can't have two 100% owners). The second purchaser's title would not be valid, even if they initially thought it was at the time of purchase.

It doesn't matter that you didn't know it was stolen - it's still not yours, it belongs to the person it was stolen from. It's your job to get your money back from the last person, and their job to get their money back from the previous person - all the way back to the thief.

If it's not possible to recover the money from the thief - wow, sucks to be you. You have a claim against the thief, but that doesn't matter if they don't have any money. You can garnish their wages from their McJob when they get out of prison.

When art or other property is stolen often collecting from the thief is not possible, there are two innocents, the most recent purchaser and the original owner. The common law principle is that a buyer cannot pass on a greater title to previously stolen property, the original owner has the superior claim. But there are some exceptions. A good faith(bona fide purchaser for value without notice) buyer obtains a lawful title, even if there are others with a competing claim to the title provided several related requirements are met. Davis v. Carroll digs in to examples of what does and does not qualify as a good faith purchase in the context of valuable art.

Also notable here is that German law, and many other European countries is opposite the English common law rule, and effectively the burden goes the other way and the scope of good faith is widened. Article 932(2) of the German Civil Code covers this for instance.

When dealing with stolen property from 50+ years ago there are issues with the statute of limitations, and with laches as well

But in this case the museum doesn't have a better claim than you do either that they aren't the thief, just an older one. In fact theirs seems worse, just a record that they possessed it at one point in the 1920s. Could be that the curators who first logged it into inventory were the original thieves in the line plundering it from someone else vs paying fairly.

In the legal perspective, none of that matters. If the artifact can be definitively proven to have belonged to X, and they were robbed, then it belongs to X regardless of who's done anything in the meantime. That's the legal answer here. The same is true of real property, or a stereo. It belongs to the person it originally belonged to, before it was stolen.

Morally, it's debatable. Legally, it's straightforward, a stolen item does not become un-stolen with time, nor does the claim of the original owner diminish. Morally that's not how people think, but legally that's how it works.

The British Museum argument does not work for plebians. It's not "yours" just because you kept it for 100 years. Nor is it the next person's because they didn't know it was stolen.

The British Museum only works for the British because they were a god-ordained royal family that controlled an empire spanning the globe, then a nuclear-armed imperial power. It was based on the rather debatable legal theory of "try and stop us". It's increasingly recognized that it's unjust and seems increasingly likely that it will be dissolved sometime in the next hundred years. Because yeah, the same arguments apply to shit the British looted as shit the Nazis looted. It's not theirs. Maybe some countries will be willing to loan them back on a permanent basis though.

It seems to me if they want to have a legitimate claim strong enough to take it from someone who legitimately purchased it, then they will need to come up with some evidence that they themselves did not steal the statue from somewhere else in the first place.