I agree, I think that is basically why he says that, and not that it ever necessarily “was his”, per se. For sure. But if you were also to base that off of his reaction, I think he may have seen it before. Sure, you could argue he may have seen it in Clone Wars holograms or whatever, but if he had never seen it in person before, I feel like he would’ve been in more disbelief. Like, “Is… that?” It’s something that he may have dreamt of having for a long time, something sacred, and suddenly this stormtrooper has it? I would expect a different reaction.

But he doesn’t even look shocked or surprised by seeing it. As soon as Finn lifts it up and ignites it, there’s no question that he knows that blade, even from a distance in the darkness.

This is just based off of his reaction. Worse case it just adds another layer to it. Until canon contradicts it I don’t think any speculation hurts as headcanon or as a working theory for a fan edit. But if they ever answer this question in future material I wouldn’t be too surprised if they did something totally different that makes little sense.