Hilchos Bikkurim 9:13

Let’s say that a non-Jew converts to Judaism while he’s having an animal slaughtered. If it was slaughtered before the conversion, he need not give the gifts; if after, then he must. In a case of doubt, he need not give the gifts because the burden of proof is on the one who wants to take property from another (i.e., the kohein would have to prove that the convert must give the gifts).

Hilchos Bikkurim 9:14

One may eat meat from an animal from which the gifts were not taken; this is not like untithed produce. The reason is because the gifts that must be given to a kohein are distinct parts of the animal. A non-kohein may not eat from the gifts without a kohein’s permission. If he violates the law and eats, damages or sells them, he need not pay for it. This is because the gifts are not the property of any particular kohein. A non-kohein who buys the gifts – even though doing so is impermissible – is allowed to eat them. This is because these gifts for the kohanim were stolen.